A282445
For n>=5, a(n) is the smallest m>=3 such that odd part of ((prime(n)^2 - prime(m)^2)/3) is prime, or a(n)=0 if there is no such m
4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 7, 3, 12, 6, 8, 4, 13, 7, 8, 4, 11, 3, 20, 5, 6, 22, 11, 23, 13, 16, 14, 9, 10, 10, 24, 29, 6, 40, 31, 0, 3, 4, 40, 11, 32, 45, 13, 7, 30, 3, 53, 20, 6, 30, 35, 27, 54, 26, 0, 63, 46, 57, 16, 67, 67, 38, 0, 39, 52, 5, 61, 75, 3
Offset: 5
Keywords
Examples
Let n=9, prime(9)=23. If m=3, then odd part of (23^2 - 5^2)/24 is 21, while if m=4, then odd part of (23^2 - 7^2)/24 is 5 which is prime. So a(9)=4.
Programs
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Mathematica
f[n_] := Block[{m = 3, p = Prime[n]^2}, While[q = (p - Prime[m]^2)/3; m < n && ! PrimeQ[q/2^IntegerExponent[q, 2]], m++]; If[m < n, m, 0]]; Array[f, 73, 5] (* Robert G. Wilson v, Feb 15 2017 *)
Extensions
More terms from Peter J. C. Moses, Feb 15 2017
Comments