A267503 - OEIS

A267503

Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 5 are also in the sequence.

2, 3, 7, 11, 23, 31, 43, 47, 67, 71, 139, 211, 283, 311, 331, 431, 463, 659, 683, 691, 863, 947, 967, 1291, 1303, 1319, 1367, 1427, 1699, 1867, 1979, 1987, 2011, 2111, 2131, 2311, 2531, 3011, 3083, 4099, 4423, 4643, 4691, 4831, 5171, 5179, 5683, 5839, 6299, 6911, 7283, 7591, 8563, 8863, 9227, 9871, 9931, 10343, 10627, 11887, 11923, 12911

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OFFSET

1,1

COMMENTS

Is this sequence infinite?

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

N:= 20000: # to get all terms <= N

Res:= 2:

Agenda:= {3, 11}:

P:= {2, 10}:

g:= proc(t) local s; s:= p*t; if s < N then s else NULL fi end proc:

while Agenda <> {} do

p:= min(Agenda);

Res:= Res, p;

newP:= map(g , P);

P:= P union newP;

Agenda:= Agenda minus {p} union select(isprime, map(`+`, newP, 1));

od:

Res; # Robert Israel, Mar 15 2019

MATHEMATICA

fa = FactorInteger; is[2, p_] = True; is[2, p_];

is[n_, p_] := PrimeQ[n] && MoebiusMu[n - 1] ≠ 0 && Union@Table[is[fa[n - 1][[i, 1]], p] || fa[n - 1][[ i, 1]] == p , {i, Length[fa[n - 1]]}] == {True}; Select[Prime[Range[10000]], is[#, 5] &]

CROSSREFS

Cf. A267504, A267505, A267506, A267507, A005117, A227455, A227007, A227006.

Sequence in context: A108184 A049091 A039787 * A226937 A227199 A129940

Adjacent sequences: A267500 A267501 A267502 * A267504 A267505 A267506

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Jan 16 2016

STATUS

approved