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%I #22 Feb 23 2022 23:07:06
%S 2,3,5,7,17,19,43,101,163,257,487,1459,14407,26407,39367,62501,65537,
%T 77659,1020101,1336337,86093443,242121643,258280327,3103616899,
%U 4528177054183,15258789062501,411782264189299,21108889701347407,953735353027359375062501
%N Primes which divide a term of A073935.
%C A prime p is in this sequence if and only if p-1 = Product_{i} (p_i)^(a_i) with p_j - 1 = Product_{j<i} (p_j)^(a_j).
%C This sequence contains all Fermat primes (A019434).
%H John Machacek, <a href="https://arxiv.org/abs/1706.01008">Egyptian Fractions and Prime Power Divisors</a>, arXiv:1706.01008 [math.NT], 2017.
%e p = 43 is in the sequence because 43-1 = 42 = 2*3*7, 7-1 = 6 = 2*3, 3-1 = 2.
%t upTo[mx_] := Block[{ric}, ric[n_, p_] := If[n < mx, Block[{m = n p}, If[PrimeQ[n + 1], Sow[n+1]; ric[n (n + 1), n+1]]; If[IntegerExponent[n, p] == 1, While[m < mx, ric[m, p]; m *= p]]]]; Sort[Reap[ric[1, 2]][[2, 1]]]]; upTo[10^20] (* _Giovanni Resta_, May 27 2017 *)
%Y Cf. A073935.
%K nonn
%O 1,1
%A _John Machacek_, May 27 2017
%E a(20)-a(29) from _Giovanni Resta_, May 27 2017