A101769 Numbers p such that p, 2p+1, 3p+2, 4p+3, 5p+4, 6p+5, 7p+6, 8p+7 are primes.

2894219, 60041519, 64523969, 242024369, 407874179, 1092040949, 1092075389, 1674689729, 2281060319, 5035134509, 5329406669, 5683382879, 5792424329, 6000216809, 6380217479, 10409580719, 11488703939, 13745865209, 14181824369, 14904963149, 15002412599, 15412603919

Offset: 1

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

• nonn
• easy

Comments

From Jeppe Stig Nielsen, Jul 07 2020: (Start)

Each term is -1 modulo 210.

The subset p, 2p+1, 4p+3, 8p+7 is a Cunningham chain, cf. A023272. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..250 (first 50 terms from Jeppe Stig Nielsen)
• Wikipedia, Cunningham chain

Crossrefs

Cf. A000040, A005384, A023272, A067256, A067257, A067258, A101767, A101768, A101769, A101770, A336060.

Programs

Maple

R:= NULL: count:= 0:
for i from 0 while count < 50 do
  for j in [1049,2099, 2309] do
    p:= 2310*i+j;
    if andmap(isprime,[p, 2*p + 1, 3*p + 2, 4*p + 3, 5*p + 4, 6*p + 5, 7*p + 6, 8*p + 7]) then
      count:= count+1; R:= R,p;
    fi
od od:
R; # Robert Israel, May 21 2025

Mathematica

a={}; Do[p=Prime[n]; If[PrimeQ[p*2+1]&&PrimeQ[p*3+2]&&PrimeQ[p*4+3]&&PrimeQ[p*5+4]&&PrimeQ[p*6+5]&&PrimeQ[p*7+6]&&PrimeQ[p*8+7], AppendTo[a, p]], {n, 1, 10^7}]; Print[a]; (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

Extensions

a(20)-a(22) from Jeppe Stig Nielsen, Jul 07 2020