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A176790
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Honaker primes of the form k^2 + 1.
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3
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3137, 4357, 13457, 80657, 115601, 184901, 309137, 341057, 1008017, 1073297, 4227137, 5541317, 11806097, 16974401, 18576101, 22848401, 24443137, 24542117, 27625537, 28132417, 30913601, 39112517, 42432197, 46049797, 46321637, 52417601, 71132357, 84713617, 92736901
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OFFSET
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1,1
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COMMENTS
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The list of associated n is: 56, 66, 116, 284, 340, 430, 556, 584, 1004, 1036, 2056, ...
The associated indices in A002496 are: 14, 15, 21, 48, 53, 61, 73, 76, 113, 115, 215, 243, 341, 395, 414, ...
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REFERENCES
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M. Aigner, Diskrete Mathematik, Vieweg u. Teubner, 6. Aufl., 2006.
E. Grosswald, Representations of Integers as Sums of Squares, Springer-Verlag, Berlin, 1985.
H. Scheid, Zahlentheorie, Spektrum Akademischer Verlag, 4. Aufl., 2006.
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LINKS
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EXAMPLE
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a(1) = 3137 = 56^2 + 1 = A033548(24).
a(2) = 4357 = 66^2 + 1 = A033548(31).
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MATHEMATICA
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fHQ[n_]:=Plus@@IntegerDigits@n==Plus@@IntegerDigits@PrimePi@n; Select[Range[10000]^2+1, PrimeQ[#] && fHQ[#] &] (* K. D. Bajpai, Apr 06 2021 *)
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PROG
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(PARI) for(n =1, 50000, my(k=n^2+1); if(isprime(k) && vecsum(digits(k))==vecsum(digits(primepi(k))), print1(k, ", "))); \\ K. D. Bajpai, Apr 06 2021
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 26 2010
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EXTENSIONS
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STATUS
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approved
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