A343192 Happy Honaker primes.

263, 1039, 1933, 2221, 3067, 3137, 5741, 6343, 6353, 6971, 7481, 8821, 9103, 10247, 11251, 12347, 13037, 13339, 13457, 13933, 14437, 16451, 17317, 18041, 21617, 26309, 26339, 30091, 30293, 31177, 32009, 34471, 35227, 36307, 36433, 37117, 41131, 41333, 41801, 43781

Offset

1,1

Comments

Intersection of A033548 and A035497 or A007770.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

263 is a Honaker prime: the number of primes up to 263 is 56 and 2 + 6 + 3 = 11 = 5 + 6. 263 is also a Happy number: iterating the sum of squares of digits terminates in 1, i.e., 263 -> 4 + 36 + 9 = 49 -> 16 + 81 = 97 -> 81 + 49 = 130 -> 1 + 9 + 0 = 10 -> 1 + 0 = 1. Thus 263 is a Happy Honaker prime.

Mathematica

Select[Prime[Range[20000]], FixedPoint[Total[IntegerDigits[#]^2] &, #, 10] == 1 && Plus @@ IntegerDigits@# == Plus @@ IntegerDigits@PrimePi@# &]

Crossrefs

Cf. A007770, A033548, A035497, A046519.

Sequence in context: A142379 A128654 A236245 * A023314 A054802 A369877

Adjacent sequences: A343189 A343190 A343191 * A343193 A343194 A343195

Keyword

nonn,base

Author

K. D. Bajpai, Apr 07 2021

Status

approved