cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A226562 Numbers which are the sum of two squared primes in exactly three ways (ignoring order).

Original entry on oeis.org

2210, 3770, 5330, 6290, 12818, 16490, 18122, 19370, 24050, 24650, 26690, 32810, 33410, 34970, 36530, 39650, 39770, 44642, 45050, 45890, 49010, 50690, 51578, 57770, 59450, 61610, 63050, 66170, 67490, 72410, 73610, 74210, 80330, 85202, 86210, 86330, 88010
Offset: 1

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Author

Henk Koppelaar, Jun 11 2013

Keywords

Comments

Suggestion: difference between successive terms is always at least 3. (With the known 115885 terms <10^9, the smallest difference is 24.) - Zak Seidov, Jun 12 2013

Examples

			2210 = 19^2 + 43^2 = 23^2 + 41^2 = 29^2 + 37^2;
		

References

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

Crossrefs

Cf. A054735 (restricted to twin primes), A037073, A069496.
Cf. A045636 (sum of two squared primes), A226539.
Cf. A214511 (least number having n representations).
Cf. A226539 (restricted to sums decomposed in exactly three ways).

Programs

  • Maple
    Prime2PairsSum := s -> select( x -> `if`(andmap(isprime, x), true, false), numtheory:-sum2sqr(s)):
    for n from 2 to 10 do
    if nops(Prime2PairsSum(n)) = 3 then print(n,Prime2PairsSum(n)) fi
    od;
  • Mathematica
    Select[Range@20000, Length[Select[ PowersRepresentations[#, 2, 2], And @@ PrimeQ[#] &]] == 3 &] (* Giovanni Resta, Jun 11 2013 *)

Extensions

a(22)-a(37) from Giovanni Resta, Jun 11 2013