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Prime numbers p such that x^2 + x + p produces primes for x = 0..8 but not x = 9.
2

%I #11 Nov 02 2021 21:11:16

%S 51867197,85776137,93685301,97122197,107599757,113575727,118136267,

%T 232728647,316973621,483040757,564537761,749930717,840472307,

%U 901288517,1559839991,1696818647,2251028567,2469604721,2796607337,3098938847,3152692841,3344410367

%N Prime numbers p such that x^2 + x + p produces primes for x = 0..8 but not x = 9.

%C The first term is A164926(9).

%H T. D. Noe, <a href="/A211237/b211237.txt">Table of n, a(n) for n = 1..500</a>

%t lookfor = 9; t = {}; n = 0; While[Length[t] < 25, n++; c = Prime[n]; i = 1; While[PrimeQ[i^2 + i + c], i++]; If[i == lookfor, AppendTo[t, c]]]; t

%t Select[Prime[Range[31*10^5,65*10^5]],AllTrue[#+{2,6,12,20,30,42,56,72},PrimeQ] && CompositeQ[#+90]&] (* The program generates the first 6 terms of the sequence. To generate more, increase the second Range constant. *) (* _Harvey P. Dale_, Nov 02 2021 *)

%Y Cf. A067774, A164926.

%K nonn

%O 1,1

%A _T. D. Noe_, Apr 08 2012