

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
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OFFSET

1,1


COMMENTS

The 2nd and 3rd repunit primes, 1111111111111111111 and 11111111111111111111111 are happy primes.  Thomas M. Green, Oct 23 2009


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 *)


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



