A087520 - OEIS

A087520

Smallest prime p such that the prime signature of p-1 has not occurred earlier.

2, 3, 5, 7, 13, 17, 31, 37, 41, 61, 73, 97, 113, 181, 193, 211, 241, 257, 271, 401, 421, 433, 541, 577, 641, 673, 769, 1009, 1153, 1297, 1321, 1801, 2017, 2113, 2161, 2311, 2341, 2377, 2521, 2593, 2689, 3121, 3361, 3457, 4001, 4357, 4621, 4801, 6301, 6481

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OFFSET

0,1

COMMENTS

Sequence is infinite, as a corollary of Dirichlet's theorem: e.g. for each k there are primes p with p-1 divisible by 2^k. - Robert Israel, Jul 09 2018

LINKS

Robert Israel, Table of n, a(n) for n = 0..500

EXAMPLE

Primes 19 and 29 are not members as the prime signature p^2*q is the same as that corresponding to the prime 13 (12, 18 and 28 have the same prime signature).

MAPLE

p:= 1: PS:= {}: Res:= NULL: count:= 0:

while count < 100 do

p:= nextprime(p);

ps:= sort(map(t -> t[2], ifactors(p-1)[2]));

if not member(ps, PS) then

count:= count+1; Res:= Res, p; PS:= PS union {ps}

od:

Res; # Robert Israel, Jul 09 2018

CROSSREFS

Cf. A087521.

Sequence in context: A152449 A048975 A009571 * A117159 A134873 A172979