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-François Alcover, Jun 14 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henk Koppelaar, Jun 13 2013
STATUS
approved