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A105451 Numbers k such that prime(k+1) == 8 (mod k).

%I A105451 #33 Sep 05 2025 01:00:18
%S A105451 1,5,15,73,75,100347,637329,27067271,179993015,1208198523,55762149023,
%T A105451 55762149103,382465573515
%N A105451 Numbers k such that prime(k+1) == 8 (mod k).
%C A105451 No additional terms up to 7 million. - _Harvey P. Dale_, Jan 23 2012
%C A105451 Integers k such that A004649(k+1) = 8. - _Michel Marcus_, Dec 30 2022
%t A105451 bb={};Do[If[8==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 1000000}];bb
%t A105451 Select[Range[700000],Mod[Prime[#+1],#]==8&] (* _Harvey P. Dale_, Jan 23 2012 *)
%o A105451 (Python)
%o A105451 from sympy import nextprime
%o A105451 def A105451(max):
%o A105451     terms = []
%o A105451     p = 3
%o A105451     for n in range(1, max+1):
%o A105451         if (p - 8) % n == 0: terms.append(n)
%o A105451         p = nextprime(p)
%o A105451     return terms
%o A105451 # _Eric M. Schmidt_, Feb 05 2013
%Y A105451 Cf. A004649, A105286, A105287, A105288, A105290, A105329.
%Y A105451 Cf. A023150 (Numbers k such that prime(n) == 8 (mod k)).
%K A105451 nonn,more,changed
%O A105451 1,2
%A A105451 _Zak Seidov_, May 02 2005
%E A105451 First two terms inserted by _Eric M. Schmidt_, Feb 05 2013
%E A105451 a(8)-a(10) from _Michel Marcus_, Dec 29 2022
%E A105451 a(11)-a(13) from _Max Alekseyev_, Aug 31 2024