OFFSET
1,1
COMMENTS
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.
REFERENCES
Jean-Marie De Koninck and Florian Luca, Analytic Number Theory: Exploring the Anatomy of Integers, American Mathematical Society, 2012, Problem 15.1, p. 263.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
EXAMPLE
5 and 7 are not in the sequence since a(1) | (5 - 1)/2 and a(2) | (7 - 1)/2.
a(3) = 11 is in the sequence since (11 - 1)/2 = 5 is not divisible by 2 or 3.
MATHEMATICA
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}]
PROG
(PARI) isok(p, va) = {q = (p-1)/2; for (k=1, #va, if (!(q % va[k]), return (0)); ); return (1); }
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 19 2017
STATUS
approved