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

%I A101769 #23 May 21 2025 12:27:41
%S A101769 2894219,60041519,64523969,242024369,407874179,1092040949,1092075389,
%T A101769 1674689729,2281060319,5035134509,5329406669,5683382879,5792424329,
%U A101769 6000216809,6380217479,10409580719,11488703939,13745865209,14181824369,14904963149,15002412599,15412603919
%N A101769 Numbers p such that p, 2p+1, 3p+2, 4p+3, 5p+4, 6p+5, 7p+6, 8p+7 are primes.
%C A101769 From _Jeppe Stig Nielsen_, Jul 07 2020: (Start)
%C A101769 Each term is -1 modulo 210.
%C A101769 The subset p, 2p+1, 4p+3, 8p+7 is a Cunningham chain, cf. A023272. (End)
%H A101769 Robert Israel, <a href="/A101769/b101769.txt">Table of n, a(n) for n = 1..250</a> (first 50 terms from Jeppe Stig Nielsen)
%H A101769 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cunningham_chain">Cunningham chain</a>
%p A101769 R:= NULL: count:= 0:
%p A101769 for i from 0 while count < 50 do
%p A101769   for j in [1049,2099, 2309] do
%p A101769     p:= 2310*i+j;
%p A101769     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
%p A101769       count:= count+1; R:= R,p;
%p A101769     fi
%p A101769 od od:
%p A101769 R; # _Robert Israel_, May 21 2025
%t A101769 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 *)
%Y A101769 Cf. A000040, A005384, A023272, A067256, A067257, A067258, A101767, A101768, A101769, A101770, A336060.
%K A101769 nonn,easy
%O A101769 1,1
%A A101769 _Jonathan Vos Post_ and _Ray Chandler_, Dec 31 2004
%E A101769 a(20)-a(22) from _Jeppe Stig Nielsen_, Jul 07 2020