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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

N. J. A. Sloane.

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 July 30 20:16 EDT 2016. Contains 275185 sequences.