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Honaker primes
A prime  $p_n$  is a Honaker prime if its index  $n$  and  $p_n$  itself have the same sum of digits.

For example,  $p_{32}=131$  is a Honaker prime because  $3+2=1+3+1$.

The two smallest Honaker primes  $p_n$  for which the sum of the digits is less than the number of digits of  $n$ are  $p_{1300010120}=30000101111$  and  $p_{1000122031021}=30000011223001$.

 $(p_{88}=457, p_{457}=3229)$  is the earliest chain of length 2. Chains of length 3 and 4 start with  $p_{248}$  and  $p_{496657}$.

The smallest prime which is Honaker in all the bases from 2 to 10 is  $p_{277308991}= 5949670231$.

The first Honaker primes are 131, 263, 457, 1039, 1049, 1091, 1301, 1361, 1433, 1571, 1913, 1933, 2141, 2221, 2273, 2441 more terms and their indexes are, 32, 56, 88, 175, 176, 182, 212, 218, 227, 248, 293, 295, 323, 331, 338, 362, respectively.

Honaker primes can also be... (you may click on names or numbers and on + to get more values)

a-pointer 1933 6301 41131 75941 77291 + 998963701 aban 131 263 457 3000379 4000379 + 999000991 alternating 2141 2707 2729 4703 4723 + 989252101 amenable 457 1049 1301 1361 1433 + 999843421 apocalyptic 1301 1933 2273 2591 3067 + 29423 arithmetic 131 263 457 1039 1049 + 9987001 balanced p. 263 7523 11731 13457 15193 + 999821261 bemirp 1091 1606081 1806061 106891601 109168901 + 169806181 c.decagonal 1361 6301 7411 61051 252001 + 995531051 c.heptagonal 1933 5741 11173 37493 124363 + 980855191 c.pentagonal 11731 139831 256801 317731 839551 + 990472801 c.square 1301 86113 97241 218461 584281 + 959176201 c.triangular 10711 265231 867541 1293169 2058619 + 955548541 Carol 1046527 Chen 131 263 1039 1049 1091 + 99973061 congruent 263 457 1039 1301 1933 + 9985231 Cunningham 3137 4357 13457 80657 115601 + 960752017 Curzon 1049 2141 2273 5741 15173 + 199820213 cyclic 131 263 457 1039 1049 + 9987001 d-powerful 2803 4153 4397 12347 13933 + 9972233 de Polignac 3433 4153 13217 13297 14437 + 99972317 deficient 131 263 457 1039 1049 + 9987001 dig.balanced 2141 2221 2707 2729 7013 + 199805033 economical 131 263 457 1039 1049 + 19984511 emirp 1091 1301 1913 1933 3067 + 199901021 equidigital 131 263 457 1039 1049 + 19984511 esthetic 34543 3212123 343456543 565454543 Eulerian 67108837 evil 263 1049 1091 1433 1913 + 999831103 fibodiv 1301 67645819 123047543 Friedman 58921 64513 78163 122503 125029 + 902563 good prime 3433 4903 6563 6653 7411 + 199022107 happy 263 1039 1933 2221 3067 + 9982211 hex 126691 333667 436627 791047 1703287 + 972162007 Hogben 5701 8011 98911 136531 145543 + 975906361 iban 1301 2141 2221 2273 2441 + 773273 inconsummate 1049 1571 2591 3137 4091 + 996011 junction 2719 4723 5009 6311 7013 + 99954551 lucky 1039 1933 2221 3229 3433 + 9985231 magnanimous 2221 8821 40427 464447 600881 + 6600227 metadrome 457 12347 13457 modest 1433 1933 5009 13037 41333 + 998111111 nialpdrome 2221 6311 6553 6653 7411 + 998831111 odious 131 457 1039 1301 1361 + 999843421 Ormiston 1913 35617 48109 97231 115631 + 999003913 palindromic 131 16661 33533 34543 91019 + 982323289 palprime 131 16661 33533 34543 91019 + 982323289 pancake 13367 24091 64621 93097 106031 + 960424879 pernicious 131 457 1039 1301 1361 + 9985231 plaindrome 457 3559 12277 12347 13339 + 345555569 prime 131 263 457 1039 1049 + 999843421 primeval 100279 Proth 3137 57089 64513 67073 138241 + 955383809 repunit 5701 8011 98911 136531 145543 + 975906361 self 457 2729 3067 6553 10559 + 999831103 self-describing 18331031 19143133 19143331 21183223 star 11353 15913 20533 60601 87121 + 981120937 strobogrammatic 111689111 160609091 166080991 609080609 661000199 666101999 strong prime 457 1049 1091 1301 1361 + 99972703 super-d 131 1049 2591 2719 3631 + 9985231 truncatable prime 3137 4397 6353 6653 7283 + 915613967 twin 1049 1091 1301 1933 2141 + 999815041 uban 17000077 26000069 37000097 39000079 50000017 + 77000081 Ulam 131 1433 4153 4903 8011 + 9973021 undulating 131 upside-down 7283 11473699 13191979 16646449 16955149 + 98746321 weak prime 131 1039 1433 1571 1913 + 99973061 weakly prime 6173731 20212327 22138349 34302127 40432489 + 945808223 zygodrome 22277 77711 1144499 2288833 4400777 + 999112211