A394621 - OEIS

A394621

Numbers k of the form k = p1 + p2 = x^2 + y^2 + p1^2, where p1 and p2 are primes, x, y are integers.

4, 5, 9, 10, 13, 14, 21, 22, 26, 33, 34, 42, 45, 46, 49, 50, 54, 62, 66, 69, 70, 74, 78, 82, 85, 86, 90, 105, 106, 110, 114, 129, 130, 134, 138, 141, 142, 146, 150, 153, 154, 158, 162, 166, 170, 174, 178, 182, 186, 194, 198, 201, 202, 206, 210, 214, 218, 222

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OFFSET

1,1

COMMENTS

Values that allow simultaneous solution to both a two prime sum and Legendre's 3 square theorem with one of the primes forming one square.

It appears odd a(n) == 1 (mod 4) and odd a(n)-2 are prime.

Additionally the sequence frequently contains adjacent pairs a(n), a(n)+1.

Conjecture: odd a(n)-2 belong to A079739.

Conjecture: odd a(n)-4 belong to A001481.

Conjecture: even a(n) belong to A145979.

LINKS

Table of n, a(n) for n=1..58.