A077762 Number of ways of pairing the squares of the numbers 1 to n with the squares of the numbers n+1 to 2n such that each pair sums to a prime. Because an odd square must always be added to an even square to obtain a prime, this sequence is the product of A077763 and A077764.
1, 1, 0, 1, 2, 0, 1, 1, 4, 8, 0, 8, 42, 28, 140, 616, 836, 180, 1416, 2542, 10960, 96048, 242204, 367587, 923949, 1145430, 2622420, 19081728, 245846500, 2934255428, 6725485476, 7722272142, 26106311490, 114470819132, 331909473776, 330258090272, 4585951400436, 37021666628450
Offset: 1
Keywords
Examples
a(5) = 2 because there are two ways: (1,4,9,16,25) + (36,49,100,81,64) = (37,53,109,97,89) and (1,4,9,16,25) + (100,49,64,81,36) = (101,53,73,97,61).
Links
- Bert Dobbelaere, Table of n, a(n) for n = 1..50
- L. E. Greenfield and S. J. Greenfield, Some Problems of Combinatorial Number Theory Related to Bertrand's Postulate, J. Integer Sequences, 1998, #98.1.2.
Formula
a(n) = permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0, depending on whether i^2 + (j+n)^2 is prime or composite, respectively. - T. D. Noe, Feb 10 2007
Extensions
More terms from Bert Dobbelaere, Sep 08 2019
Comments