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

1,1

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

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 *)

Crossrefs

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

Sequence in context: A321669 A237944 A101768 * A237210 A209795 A246054

Adjacent sequences: A101766 A101767 A101768 * A101770 A101771 A101772

Keyword

nonn,easy

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Extensions

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

Status

approved