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A287060 Primes a(n) such that a(1) = 2, a(2) = 3, and a(n) is the smallest prime greater than a(n-1) such that (a(n) - 1)/2 is not divisible by a(m) for all m < n.

%I A287060 #18 May 27 2017 05:26:45
%S A287060 2,3,11,47,59,71,83,107,131,179,191,227,239,251,311,347,431,443,467,
%T A287060 491,563,587,599,647,719,743,839,911,971,1019,1031,1091,1103,1151,
%U A287060 1187,1259,1283,1307,1319,1367,1427,1451,1511,1523,1559,1571,1583,1619,1667
%N A287060 Primes a(n) such that a(1) = 2, a(2) = 3, and a(n) is the smallest prime greater than a(n-1) such that (a(n) - 1)/2 is not divisible by a(m) for all m < n.
%C A287060 As in A100564, the number of terms in this sequence which do not exceed x is ~ (1 + o(1)) x/(logx loglogx), thus the sum of the their reciprocals diverges.
%D A287060 Jean-Marie De Koninck and Florian Luca, Analytic Number Theory: Exploring the Anatomy of Integers, American Mathematical Society, 2012, Problem 15.1, p. 263.
%H A287060 Amiram Eldar, <a href="/A287060/b287060.txt">Table of n, a(n) for n = 1..1000</a>
%e A287060 5 and 7 are not in the sequence since a(1) | (5 - 1)/2 and a(2) | (7 - 1)/2.
%e A287060 a(3) = 11 is in the sequence since (11 - 1)/2 = 5 is not divisible by 2 or 3.
%t A287060 a[1] = 2; a[2] = 3; a[n_] := a[n] = Block[{k=PrimePi[a[n - 1]] + 1, t=Table[a[i], {i, n-1}]}, While[Union[ Mod[(Prime[k] - 1)/2, t]][[1]] == 0, k++]; Prime[k]]; Table[a[n], {n, 49}]
%o A287060 (PARI) isok(p, va) = {q = (p-1)/2; for (k=1, #va, if (!(q % va[k]), return (0));); return (1);}
%o A287060 lista(nn) = {va = [2, 3]; print1(va[1], ", " va[2], ", "); for (n=3, nn, forprime(p=nextprime(vecmax(va)+1),, if (isok(p, va), va = concat(va, p); print1(p, ", "); break);););} \\ _Michel Marcus_, May 21 2017
%Y A287060 Cf. A100564.
%K A287060 nonn
%O A287060 1,1
%A A287060 _Amiram Eldar_, May 19 2017