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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. 1

%I

%S 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,

%T 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,

%U 27,54,26,0,63,46,57,16,67,67,38,0,39,52,5,61,75,3

%N 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.

%C 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

%e 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.

%t 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 *)

%Y Cf. A000265, A024702, A075888, A282594.

%K nonn

%O 5,1

%A _Vladimir Shevelev_, Feb 15 2017

%E More terms from _Peter J. C. Moses_, Feb 15 2017

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Last modified January 29 04:46 EST 2020. Contains 331335 sequences. (Running on oeis4.)