A278585 Numbers k such that k+1 is a prime, k+2 is twice a prime, k+3 is three times a prime, and k+4 is four times a prime.

12720, 16920, 19440, 24480, 49680, 61560, 104160, 229320, 255360, 259680, 266400, 291720, 298200, 311040, 331920, 419400, 423480, 436800, 446880, 471240, 525240, 532800, 539400, 581520, 600600, 663600, 704160, 709920, 783720, 867000, 904800, 908040, 918360

Offset: 1

Author

N. J. A. Sloane, Nov 30 2016

Keywords

• nonn

Comments

a(n) == 0 mod 120 (see comment in A163573). - Chai Wah Wu, Nov 30 2016

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10001

Crossrefs

Equals A163573(n) - 1.

Cf. A036570, A074200.

Positions of terms >= 4 in A278500, thus a subsequence of A278583, A089965 and A006093.

Programs

Mathematica

Select[Range[920000],AllTrue[{#+1,(#+2)/2,(#+3)/3,(#+4)/4},PrimeQ]&] (* Harvey P. Dale, Aug 08 2021 *)

PARI

is(k)=k%120==0 && isprime(k+1) && isprime(k/2+1) && isprime(k/3+1) && isprime(k/4+1) \\ Charles R Greathouse IV, Dec 03 2016

Python

from sympy import prime, isprime
A278585_list = [4*q-4 for q in (prime(i) for i in range(1,10000)) if isprime(4*q-3) and isprime(2*q-1) and (not (4*q-1) % 3) and isprime((4*q-1)//3)] # Chai Wah Wu, Nov 30 2016