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A035497
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Happy primes: primes that eventually reach 1 under iteration of "x -> sum of squares of digits of x".
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10
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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
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1,1
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COMMENTS
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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
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REFERENCES
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R. K. Guy, Unsolved Problems Number Theory, Sect. E34.
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(PARI) has(n)=while(n>6, n=norml2(digits(n))); n==1
(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)]
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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