A member of a pair of consecutive numbers such that the sums of their prime factors are also consecutive. more
The first 600 eRAPs :
2,
3,
4,
9,
20,
24,
98,
170,
1104,
1274,
2079,
2255,
3438,
4233,
4345,
4716,
5368,
7105,
7625,
10620,
13350,
13775,
14905,
20220,
21385,
23408,
25592,
26123,
28518,
30457,
34945,
35167,
38180,
45548,
49230,
51911,
52206,
53456,
56563,
61456,
65429,
66585,
67123,
68479,
69874,
71284,
75648,
76640,
77314,
78524,
82946,
86135,
90243,
96255,
98841,
121539,
134199,
154192,
162810,
172255,
175354,
175863,
177122,
182939,
194403,
197110,
200384,
203634,
211551,
218495,
220124,
229581,
233090,
236282,
238017,
239267,
243494,
247475,
258995,
263145,
265225,
283590,
287615,
295274,
295640,
298082,
300294,
322234,
326451,
327568,
329759,
331583,
335793,
336106,
367288,
386169,
392034,
422065,
429385,
429802,
430604,
458488,
475968,
490467,
495362,
527615,
531006,
544119,
551056,
552293,
558531,
585310,
585599,
595560,
596884,
616225,
616230,
680350,
692750,
702800,
703684,
709929,
723634,
731934,
757053,
757375,
759913,
765346,
775935,
793809,
801619,
801648,
804310,
829512,
831416,
847692,
852840,
865692,
877528,
888994,
895762,
921172,
958112,
958867,
976096,
977795,
977895,
978751,
991248,
1001428,
1017784,
1032274,
1081713,
1084017,
1124711,
1135230,
1136754,
1179800,
1198224,
1204334,
1220549,
1246266,
1279530,
1282800,
1340067,
1341031,
1358863,
1366370,
1391234,
1395341,
1403669,
1424951,
1443609,
1444074,
1444960,
1452582,
1460265,
1478958,
1483233,
1500004,
1510224,
1547265,
1572827,
1576003,
1587966,
1613079,
1617190,
1662483,
1730404,
1744522,
1756907,
1808000,
1836964,
1850914,
1853774,
1860194,
1891135,
1893073,
1928457,
1961575,
1971268,
1975567,
1980874,
2009519,
2021200,
2029816,
2044998,
2065590,
2073357,
2076959,
2155583,
2192767,
2195325,
2270359,
2277754,
2303841,
2308300,
2338375,
2372792,
2373646,
2379768,
2405500,
2406431,
2412053,
2417674,
2469036,
2474384,
2489950,
2492948,
2503497,
2507040,
2510748,
2511495,
2520917,
2525457,
2527900,
2530229,
2552012,
2556714,
2578796,
2589845,
2619981,
2640146,
2641681,
2659734,
2671245,
2748127,
2806354,
2809688,
2823380,
2826845,
2842431,
2843434,
2849520,
2857394,
2917321,
2973095,
3000815,
3001407,
3002346,
3010776,
3044267,
3058264,
3060425,
3100689,
3107759,
3147630,
3183887,
3184016,
3187953,
3246724,
3258195,
3288815,
3305522,
3314439,
3318721,
3350724,
3352546,
3443825,
3509261,
3519312,
3521174,
3529074,
3540580,
3547474,
3548074,
3587744,
3620874,
3659622,
3706084,
3734374,
3767535,
3808976,
3815841,
3842794,
3843187,
3880084,
3889911,
3970889,
3972815,
4009826,
4022271,
4058769,
4060224,
4060329,
4125849,
4144387,
4196549,
4207346,
4276129,
4282500,
4291448,
4329561,
4341194,
4381203,
4383785,
4405263,
4481250,
4481344,
4513145,
4571618,
4572855,
4600802,
4649193,
4671941,
4679295,
4680389,
4687535,
4730409,
4780416,
4792367,
4854550,
4865272,
4889378,
4891521,
4955587,
4970047,
5003674,
5036655,
5100917,
5126484,
5160894,
5161900,
5269705,
5308929,
5311426,
5337555,
5355033,
5365376,
5383905,
5386899,
5405823,
5420722,
5447540,
5462218,
5464514,
5490540,
5596013,
5624575,
5625823,
5627215,
5627350,
5633044,
5643170,
5675092,
5681934,
5772898,
5806264,
5822545,
5829435,
5843225,
5847231,
5858145,
5880249,
6005852,
6019926,
6045948,
6050742,
6053963,
6069479,
6109533,
6123424,
6124521,
6142830,
6161144,
6162803,
6165272,
6201294,
6217899,
6224499,
6225232,
6239524,
6275378,
6309810,
6420548,
6436449,
6462078,
6490784,
6504514,
6531668,
6551295,
6568809,
6582390,
6591657,
6634875,
6637081,
6659443,
6773624,
6786993,
6798077,
6823288,
6828627,
6842692,
6847686,
6910851,
6917598,
6921702,
6952959,
6954824,
6968928,
6981308,
7038143,
7054474,
7118010,
7135428,
7147158,
7183106,
7183407,
7213038,
7220925,
7254745,
7288977,
7332879,
7360524,
7363400,
7396532,
7459980,
7468422,
7474960,
7552063,
7626822,
7699559,
7707654,
7718787,
7745070,
7927072,
8000286,
8052270,
8084748,
8109647,
8112752,
8115470,
8169073,
8189881,
8217489,
8292111,
8326378,
8419990,
8438840,
8456877,
8461664,
8500599,
8505567,
8540862,
8560638,
8567499,
8646550,
8646560,
8698898,
8748256,
8770112,
8867782,
9018944,
9054324,
9087394,
9100750,
9167248,
9205599,
9212381,
9218001,
9307440,
9351675,
9355256,
9449656,
9472585,
9548692,
9585488,
9625397,
9695764,
9748105,
9750699,
9819095,
9838084,
9841625,
9903632,
9952712,
9960047,
10001250,
10012410,
10046015,
10053337,
10069260,
10083499,
10121579,
10178700,
10261719,
10262095,
10298568,
10316257,
10321129,
10326606,
10360391,
10429041,
10445250,
10458539,
10474595,
10498202,
10502904,
10530162,
10546292,
10566787,
10709427,
10718925,
10721676,
10797599,
10819655,
10851523,
10884224,
10910924,
10925791,
10929674,
10997379,
11005270,
11074258,
11089168,
11093225,
11165868,
11168849,
11179201,
11192726,
11221705,
11309165,
11321810,
11386083,
11431199,
11525619,
11563096,
11574218,
11592089,
11666307,
11676734,
11702124,
11806124,
11840092,
11886404,
11899650,
11902013,
11976898,
11984401,
12067994,
12069714,
12094010,
12149024,
12316086,
12330625,
12374112,
12568899,
12596554,
12604850,
12620454,
12665679,
12732270,
12737417,
12754234,
12757882,
12784017,
12813033,
12819135,
12829940,
12875555,
12882815,
13100132,
13213225,
13224804,
13237254,
13264404,
13293422,
13301007,
13312271,
13355879,
13475240,
13492346,
13502810,
13522033,
13595885,
13638976,
13656841,
13658224,
13841905,
13870875.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 446139 values, from 2 to 999999387423).
n\r | 0 | 1 |
2 | 224898 | 221241 | 2 |
3 | 163066 | 121197 | 161876 | 3 |
4 | 126186 | 97025 | 98712 | 124216 | 4 |
5 | 109609 | 74887 | 76659 | 75058 | 109926 | 5 |
6 | 79877 | 58748 | 82572 | 83189 | 62449 | 79304 | 6 |
7 | 85260 | 55655 | 55384 | 55368 | 55336 | 55449 | 83687 | 7 |
8 | 71021 | 55966 | 50014 | 54105 | 55165 | 41059 | 48698 | 70111 | 8 |
9 | 65262 | 40400 | 48918 | 49328 | 40469 | 48039 | 48476 | 40328 | 64919 | 9 |
10 | 53536 | 37621 | 38698 | 38148 | 58488 | 56073 | 37266 | 37961 | 36910 | 51438 | 10 |
11 | 58786 | 36280 | 36475 | 36715 | 36559 | 36462 | 36301 | 36323 | 36432 | 36443 | 59363 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.