A267504 -id:A267504 - cp's OEIS frontend

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

Offset: 1

José María Grau Ribas, Jan 16 2016

nonn

Is this sequence infinite?

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

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

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

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] &]

A267505 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 13 are also in the sequence.

Original entry on oeis.org

2, 3, 7, 43, 79, 547, 3319, 6163, 36979, 42667, 258847, 1553119, 1573207, 1834639, 1854763, 11131927, 20224159, 20451679, 124027567, 141569107, 141588763, 467477683, 1840398379, 3278780359, 5276533183, 6089163523, 6155955079, 11168428363, 11185512199, 31655671459

Offset: 1

José María Grau Ribas, Jan 16 2016

nonn

Is this sequence infinite?

Andrew Howroyd, Table of n, a(n) for n = 1..500

Cf. A267503, A267504, A267506, A267507, A005117, A227455, A227007, A227006.

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[100000]], is[#, 13] &]

leastdiv(v, pred, inf)={ \\ finds least divisor d satisfying pred(d) && d>=inf
  my(recurse(k,d,lim)= if(d >= lim, lim, if(d>=inf && pred(d), d, k++; if(k<=#v, lim=self()(k, d*v[k], lim); self()(k, d, lim), lim))));
  my(stop=vecprod(v), lim=inf, m=4);
  while(lim<=stop, lim*=m; my(d=recurse(0,1,lim)); if(disprime(d+1), S[#S]); if(t==oo, break); t++; print1(t, ", "))} \\ Andrew Howroyd, Nov 13 2018

Terms a(16) and beyond from Andrew Howroyd, Nov 13 2018

A267507 Prime numbers n such that n-1 is squarefree and all prime divisors of n-1 other than 19 are in the sequence.

Original entry on oeis.org

2, 3, 7, 43, 4903, 168241543, 5773040306503

Offset: 1

José María Grau Ribas, Jan 16 2016

Cf. A267503, A267504, A267505, A267506, A267507.

S[1] = {2, 19}; PR[S_] := Product[S[[i]], {i, Length[S]}];
S[m_] := S[m] =  Union[S[m - 1], Select[Table[PR[Subsets[S[m - 1]] [[i]]] + 1, {i, 2^Length[S[m - 1]]}], PrimeQ]]; A267507 = Complement[S[7], {19}]
(* S[7]=S[8] ==> sequence is finite and full; José María Grau Ribas, Nov 22 2021 *)

A267506 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 17 are also in the sequence.

Original entry on oeis.org

2, 3, 7, 43, 103, 239, 479, 619, 3347, 4327, 10039, 24379, 25999, 30703, 48859, 123583, 143879, 147703, 150587, 170647, 186019, 288359, 344639, 421639, 593003, 689279, 690719, 1029827, 1381439, 1779007, 2651899, 3089479, 3558019, 4242983

Offset: 1

José María Grau Ribas, Jan 16 2016

nonn

Is this sequence infinite?

Cf. A267503, A267504, A267505, A267507, A005117, A227455, A227007, A227006.

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[#, 17] &]

cp's OEIS Frontend

A267503 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 5 are also in the sequence.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A267505 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 13 are also in the sequence.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A267507 Prime numbers n such that n-1 is squarefree and all prime divisors of n-1 other than 19 are in the sequence.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A267506 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 17 are also in the sequence.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica