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<n.

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

5,1

Comments

a(n) = 0 for n: 44, 63, 71, 80, 89, 95, 97, 108, 118, 122, 132, 141, 150, etc. Robert G. Wilson v, Feb 15 2017

Links

Table of n, a(n) for n=5..77.

Example

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.

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 *)

Crossrefs

Cf. A000265, A024702, A075888, A282594.

Sequence in context: A187470 A059124 A320604 * A281705 A026858 A188885

Adjacent sequences: A282442 A282443 A282444 * A282446 A282447 A282448

Keyword

nonn

Author

Vladimir Shevelev, Feb 15 2017

Extensions

More terms from Peter J. C. Moses, Feb 15 2017

Status

approved