A260758 Least k > 0 such that M(n)^2 + 2k is prime, where M(n) = 2^n - 1 = A000225(n).
1, 1, 1, 2, 1, 3, 10, 5, 1, 3, 14, 11, 4, 5, 4, 5, 8, 30, 2, 6, 1, 8, 29, 12, 29, 30, 11, 2, 4, 5, 19, 29, 2, 9, 7, 11, 4, 74, 16, 24, 8, 18, 10, 30, 56, 15, 35, 24, 4, 35, 19, 111, 19, 18, 1, 57, 8, 20, 14, 2, 2, 48, 29, 26, 92, 24, 19, 155, 2, 78, 35, 56, 113, 33, 70, 32, 7
Offset: 0
Keywords
Examples
M(0)^2 + 2*1 = 0 + 2 = 2 is prime, thus a(0)=1. M(1)^2 + 2*1 = 1 + 2 = 3 is prime, thus a(1)=1. M(2) = 2^2-1 = 3 and 3*3 + 2k = 11 is a prime for k=1, thus a(2) = 1. M(3) = 2^3-1 = 7 and 7*7 + 2k = 53 is a prime for k=2 but not for k=1, thus a(3) = 2. M(4) = 2^4-1 = 15 and 15*15 + 2k = 227 is a prime for k=1, thus a(4) = 1.
Crossrefs
Cf. A260757.
Programs
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PARI
a(n)=for(k=1,9e9,ispseudoprime((2^n-1)^2+2*k)&&return(k))