A237189 Numbers k such that k+1, 2k+1, 3k+1, 4k+1 are all prime.

330, 1530, 3060, 4260, 4950, 6840, 10830, 15390, 18120, 23010, 25410, 26040, 31770, 33300, 40110, 41490, 45060, 49830, 53880, 59340, 65850, 70140, 73770, 78540, 88740, 95460, 96930, 109470, 111720, 112620, 117720, 131310, 133200, 134730, 135300, 150150, 165900

Offset

1,1

Comments

A subsequence of A064238.

All terms are divisible by 30, and b(n)=a(n)/30 begins: 11, 51, 102, 142, 165, 228, 361, 513, 604, 767, 847, 868, 1059, 1110, 1337, 1383, 1502, 1661, 1796, 1978, 2195, ...

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Giovanni Resta)

Formula

a(n) = 2*(A105653(n) + 1) = 2*A124409(n). - Hugo Pfoertner, May 03 2021

Prog

(Python)
import sympy
from sympy import isprime
for n in range(0, 100000, 2):
    if isprime(n+1) and isprime(2*n+1) and isprime(3*n+1) and isprime(4*n+1):
        print(str(n), end=', ')

Crossrefs

Cf. A088250, A064238, A105653, A124409.

Sequence in context: A300009 A244264 A117345 * A064262 A126997 A205993

Adjacent sequences: A237186 A237187 A237188 * A237190 A237191 A237192

Keyword

nonn

Author

Alex Ratushnyak, Feb 04 2014

Status

approved