A208295 a(n)*(a(n)+1) + A002973(n)^2 = A005098(n), n>=1.

0, 1, 0, 2, 0, 2, 3, 2, 1, 2, 4, 0, 1, 3, 5, 3, 5, 6, 4, 3, 0, 7, 6, 7, 0, 6, 4, 2, 8, 6, 5, 4, 2, 8, 3, 8, 9, 0, 1, 7, 8, 3, 10, 9, 2, 5, 10, 9, 6, 0, 11, 2, 8, 9, 12, 6, 12, 11, 0, 2, 7, 13, 4, 9, 12

Offset: 1

Author

Wolfdieter Lang, Mar 01 2012

Keywords

• nonn

Comments

See the Jon Perry comment on A005098. The (even) promic number a(n)*(a(n)+1) (see A002378) when subtracted from A005098(n) (the n-th value k such that 4*k+1 is prime) leaves a square, namely A002973(n)^2. E.g., n=4: 7 - 2*3 = 1^1. n=5: 9 - 0 = 3^2.

2*a(n)+1 = A002972(n), n>=1. E.g., n=4: 2*2+1=5.

Crossrefs

Cf. A005098, A002144, A002972, A002973, A002378.

Formula

a(n) = (sqrt(4*(k(n) - m(n)^2)+1)-1)/2, n>=1, with k(n) := A005098(n) (4*k(n)+1 is the prime A002144(n)) and m(n):= A002973(n).

a(n) = (A002972(n)-1)/2, n>=1.