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 A035497 Happy primes: primes that eventually reach 1 under iteration of "x -> sum of squares of digits of x". 8
 7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563, 617, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1009, 1033, 1039, 1093, 1151, 1277, 1303, 1373, 1427, 1447, 1481, 1487, 1511, 1607, 1663 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The 2nd and 3rd repunit primes, 1111111111111111111 and 11111111111111111111111 are happy primes. - Thomas M. Green, Oct 23 2009 There are 200 terms up to 10^4, 1465 up to 10^5, 11144 up to 10^6, 91323 up to 10^7, 812371 up to 10^8, 7408754 up to 10^9, and 67982202 up to 10^10. These are consistent with b*prime(n) < a(n) < c*prime(n) with constants 0 < b < c. - Charles R Greathouse IV, Jan 06 2016 REFERENCES R. K. Guy, Unsolved Problems Number Theory, Sect. E34. LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..10000 C. Rivera, Related puzzle page Eric Weisstein's World of Mathematics, Happy Number Wikipedia, Happy number Doctor Who, Episode 42 Wikipedia, Doctor Who, Episode 42 MATHEMATICA g[n_] := Total[ IntegerDigits[n]^2]; fQ[n_] := NestWhileList[g@# &, n, UnsameQ, All][[-1]] == 1; Select[Prime@ Range@ 300, fQ@# &] (* Robert G. Wilson v, Jan 03 2013 *) PROG (PARI) has(n)=while(n>6, n=norml2(digits(n))); n==1 is(n)=has(n) && isprime(n) \\ Charles R Greathouse IV, Dec 14 2015 CROSSREFS Cf. A007770 (happy numbers), A046519. Sequence in context: A209623 A058620 A038910 * A216527 A059335 A070419 Adjacent sequences:  A035494 A035495 A035496 * A035498 A035499 A035500 KEYWORD nonn,easy,base AUTHOR EXTENSIONS More terms from Patrick De Geest, Oct 15 1999. Doctor Who links from David Applegate, Oct 06 2008 STATUS approved

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Last modified December 12 23:32 EST 2018. Contains 318081 sequences. (Running on oeis4.)