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 A035497 Happy primes: primes that eventually reach 1 under iteration of "x -> sum of squares of digits of x". 10
 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 Carlos Rivera, Puzzle 21. Happy primes, The Prime Puzzles and Problems Connection. Eric Weisstein's World of Mathematics, Happy Number Doctor Who, Episode 42 Wikipedia, Happy number 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 *) hpQ[p_]:=NestWhile[Total[IntegerDigits[#]^2]&, p, #!=1&, 1, 50]==1; Select[Prime[ Range[ 300]], hpQ] (* Harvey P. Dale, Jun 07 2022 *) 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 (Python) from sympy import isprime def swb(n): return sum(map(lambda x: x*x, map(int, str(n)))) def happy(bd): while bd not in [1, 4]: bd = swb(bd) # iterate to fixed point or cycle return bd == 1 def ok(n): return isprime(n) and happy(n) def aupto(n): return [k for k in range(1, n+1) if ok(k)] print(aupto(2012)) # Michael S. Branicky, Jul 13 2022 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 N. J. A. Sloane EXTENSIONS More terms from Patrick De Geest, Oct 15 1999 STATUS approved

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Last modified September 22 18:10 EDT 2023. Contains 365531 sequences. (Running on oeis4.)