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A226599 Numbers which are the sum of two squared primes in exactly four ways (ignoring order). 1
10370, 10730, 11570, 12410, 13130, 19610, 22490, 25010, 31610, 38090, 38930, 39338, 39962, 40970, 41810, 55250, 55970, 59330, 59930, 69530, 70850, 73730, 76850, 77090, 89570, 98090, 98930, 103298, 118898, 125450, 126290, 130730, 135218, 139490 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It appears that all first differences are divisible by 24. - Zak Seidov, Jun 14 2013

REFERENCES

Stan Wagon, Mathematica in Action, Springer, 2000 (2nd ed.), Ch. 17.5, pp. 375-378.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = p^2 + q^2; p, q are (not necessarily different) primes

EXAMPLE

10370 = 13^2 + 101^2 = 31^2 + 97^2 = 59^2 + 83^2 = 71^2 + 73^2.

10730 = 11^2 + 103^2 = 23^2 + 101^2 = 53^2 + 89^2 = 67^2 + 79^2.

MAPLE

Prime2PairsSum := s -> select(x ->`if`(andmap(isprime, x), true, false),

   numtheory:-sum2sqr(s)):

for n from 2 to 10^6 do

  if nops(Prime2PairsSum(n)) = 4 then print(n, Prime2PairsSum(n)) fi;

od;

MATHEMATICA

(* Assuming mod(a(n), 24) = 2 *) Reap[ For[ k = 2, k <= 2 + 240000, k = k + 24, pr = Select[ PowersRepresentations[k, 2, 2], PrimeQ[#[[1]]] && PrimeQ[#[[2]]] &]; If[Length[pr] == 4 , Print[k]; Sow[k]]]][[2, 1]] (* Jean-Fran├žois Alcover, Jun 14 2013 *)

CROSSREFS

Cf. A054735 (restricted to twin primes), A037073, A069496.

Cf. A045636 (sum of two squared primes is a superset).

Cf. A214511 (least number having n representations).

Cf. A225104 (numbers having at least three representations is a superset).

Cf. A226539, A226562 (sums decomposed in exactly two and three ways).

Sequence in context: A234907 A180460 A035912 * A305332 A271766 A104439

Adjacent sequences:  A226596 A226597 A226598 * A226600 A226601 A226602

KEYWORD

nonn

AUTHOR

Henk Koppelaar, Jun 13 2013

STATUS

approved

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Last modified September 25 07:27 EDT 2021. Contains 347654 sequences. (Running on oeis4.)