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

Author

Alex Ratushnyak, Feb 04 2014

Keywords

• nonn

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)

Crossrefs

Cf. A088250, A064238, A105653, A124409.

Programs

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=',')

Formula

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