A176790 - OEIS

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

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OFFSET

1,1

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, ...

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

EXAMPLE

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

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

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Sequence in context: A061048 A250849 A238499 * A086103 A267721 A031554

Adjacent sequences: A176787 A176788 A176789 * A176791 A176792 A176793

KEYWORD

base,nonn

AUTHOR

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

EXTENSIONS

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

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

STATUS

approved