A338416 Numbers k such that both 3*k-2 and 2*k-3 are in A338410.

11, 71, 1091, 2927, 7127, 12347, 23087, 41651, 56951, 74747, 119771, 234947, 298451, 405287, 458207, 649907, 656291, 708371, 936587, 991187, 1015127, 1056971, 1058807, 1128527, 1129787, 1169687, 1393967, 1413371, 1417067, 1442351, 1502747, 1707551, 1752227, 1785071, 1928807, 1957871, 1998947

Offset

1,1

Comments

Primes p such that 3*p-2, 2*p-3, (3*p+1)/2 and (2*p-1)/3 are all prime.

All terms == 11 (mod 12).

Links

Robert Israel, Table of n, a(n) for n = 1..4000

Example

a(3) = 1091 is in the sequence because 3*1091-2=3271 and 2*1091-3=2179 are in A338410.

Maple

filter:= proc(p) isprime(p) and isprime(3*p-2) and isprime(2*p-3) and isprime((3*p+1)/2) and isprime((2*p-1)/3) end proc:
select(filter, [seq(i, i=11 .. 10^7, 12)]);

Mathematica

Select[Prime[Range[150000]], AllTrue[{3#-2, 2#-3, (2#-1)/3, (3#+1)/2}, PrimeQ]&] (* Harvey P. Dale, May 20 2023 *)

Crossrefs

Cf. A338410.

Sequence in context: A139185 A103998 A160587 * A034196 A236173 A092044

Adjacent sequences: A338413 A338414 A338415 * A338417 A338418 A338419

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Oct 25 2020

Status

approved