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eRAPs
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 
2224898221241 2 
3163066121197161876 3 
41261869702598712124216 4 
5109609748877665975058109926 5 
6798775874882572831896244979304 6 
785260556555538455368553365544983687 7 
87102155966500145410555165410594869870111 8 
9652624040048918493284046948039484764032864919 9 
1053536376213869838148584885607337266379613691051438 10 
115878636280364753671536559364623630136323364323644359363

A pictorial representation of the table above
motab
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.