A176790 Honaker primes of the form k^2 + 1.

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

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 26 2010

Keywords

• base
• nonn

Comments

The intersection of A033548 with A002522 or with A002496.

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, ...

Examples

			a(1) = 3137 = 56^2 + 1 = A033548(24).
a(2) = 4357 = 66^2 + 1 = A033548(31).
		

References

• 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.

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1570

Crossrefs

Cf. A000040, A002496, A033548, A176012, A176111, A176465.

Programs

Mathematica

fHQ[n_]:=Plus@@IntegerDigits@n==Plus@@IntegerDigits@PrimePi@n;Select[Range[10000]^2+1, PrimeQ[#] && fHQ[#] &]  (* K. D. Bajpai, Apr 06 2021 *)

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

Extensions

Comments tightened by R. J. Mathar, Jun 07 2010

a(21)-a(29) from K. D. Bajpai, Apr 06 2021