A286499 Primes which divide a term of A073935.

2, 3, 5, 7, 17, 19, 43, 101, 163, 257, 487, 1459, 14407, 26407, 39367, 62501, 65537, 77659, 1020101, 1336337, 86093443, 242121643, 258280327, 3103616899, 4528177054183, 15258789062501, 411782264189299, 21108889701347407, 953735353027359375062501

Offset

1,1

Comments

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).

This sequence contains all Fermat primes (A019434).

Links

Table of n, a(n) for n=1..29.

John Machacek, Egyptian Fractions and Prime Power Divisors, arXiv:1706.01008 [math.NT], 2017.

Example

p = 43 is in the sequence because 43-1 = 42 = 2*3*7, 7-1 = 6 = 2*3, 3-1 = 2.

Mathematica

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 *)

Crossrefs

Cf. A073935.

Sequence in context: A142885 A108547 A319823 * A116947 A066277 A360383

Adjacent sequences: A286496 A286497 A286498 * A286500 A286501 A286502

Keyword

nonn

Author

John Machacek, May 27 2017

Extensions

a(20)-a(29) from Giovanni Resta, May 27 2017

Status

approved