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A286499 Primes which divide a term of A073935. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A prime p is in this sequence if and only if p-1 = prod_i (p_i)^(a_i) with p_j - 1 = prod_(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 A164134

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

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)