A224612 - OEIS

A224612

Let p = prime(n). Smallest j such that q = j*2*p^3-1, r = j*p*2*q^2-1, s = j*p*2*r^2-1, and j*p*2*s^2-1 are prime numbers.

29952, 12063, 1463, 6102, 11661, 49552, 639179, 2099290, 291248, 393186, 545251, 321303, 436641, 278295, 746832, 237852, 56490, 165901, 152847, 619755, 777177, 3410085, 117513, 2015421, 497170, 14750, 161190, 347039, 251835, 57536, 222, 2083286, 384944, 1228474, 3909960, 344164, 332224, 207751, 14060

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Conjecture: a(n) exists for all n.

LINKS

Table of n, a(n) for n=1..39.

MAPLE

f:= proc(n) local j, p, q, r, s;

p:= ithprime(n);

for j from 1 do

q:= j*2*p^3-1; if not isprime(q) then next fi;

r:= j*p*2*q^2-1; if not isprime(r) then next fi;

s:= j*p*2*r^2-1; if not isprime(s) then next fi;

if isprime(j*p*2*s^2-1) then return j fi;

end proc;

map(f, [$1..25]); # Robert Israel, May 15 2025

MATHEMATICA

a[n_] := For[j = 1, j < 10^7, j++, p = Prime[n]; If[PrimeQ[q = j*2*p^3 - 1] && PrimeQ[r = j*2*p*q^2 - 1] && PrimeQ[s = j*2*p*r^2 - 1] && PrimeQ[j*2*p*s^2 - 1], Return[j]]]; Table[Print[an = a[n]]; an, {n, 1, 24}] (* Jean-François Alcover, Apr 12 2013 *)

CROSSREFS

Cf. A224492, A224609, A224610, A224611.

Sequence in context: A235826 A235823 A235581 * A233946 A234735 A106771

Adjacent sequences: A224609 A224610 A224611 * A224613 A224614 A224615

KEYWORD

nonn

AUTHOR

Pierre CAMI, Apr 12 2013

EXTENSIONS

More terms from Jean-François Alcover, Apr 12 2013

Name clarified and more terms from Robert Israel, May 15 2025

STATUS

approved