cp's OEIS Frontend

A105286 Numbers k such that prime(k+1) == 1 (mod k).

%I A105286 #41 Aug 31 2024 21:46:13
%S A105286 1,2,3,10,24,25,66,168,182,186,187,188,438,6462,40071,40084,40085,
%T A105286 40091,40108,40118,251745,637224,637306,637336,637338,10553441,
%U A105286 10553445,10553452,10553479,10553515,10553550,10553829,27067032,27067054,27067134,69709710,69709713,179992838,179993008,3140421868,8179002150,55762149074,1003652347080,1003652347109,1003652347112,1003652347352,1003652347375
%N A105286 Numbers k such that prime(k+1) == 1 (mod k).
%C A105286 If k is a term, then prime(k+1)^prime(k+1) is a reverse Meertens number in base prime(k+1)^((prime(k+1)-1)/k). - _Chai Wah Wu_, Dec 14 2022
%C A105286 Integers k such that A004649(k+1) = 1. - _Michel Marcus_, Dec 30 2022
%H A105286 Chai Wah Wu, <a href="http://arxiv.org/abs/1603.08493">Meertens Number and Its Variations</a>, arXiv:1603.08493 [math.NT], 2016.
%H A105286 Chai Wah Wu, <a href="https://research.library.kutztown.edu/contact/vol3/iss1/5">Meertens number and its variations</a>, Communications on Number Theory and Combinatorial Theory, 3 (2022), article 5.
%t A105286 bb={};Do[If[1==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 200000}];bb
%o A105286 (Sage)
%o A105286 def A105286(max) :
%o A105286     terms = []
%o A105286     p = 3
%o A105286     for n in range(1, max+1) :
%o A105286         if (p - 1) % n == 0 : terms.append(n)
%o A105286         p = next_prime(p)
%o A105286     return terms
%o A105286 # _Eric M. Schmidt_, Feb 05 2013
%o A105286 (Python)
%o A105286 from itertools import count, islice
%o A105286 from sympy import prime
%o A105286 def A105286_gen(startvalue=1): # generator of terms >= startvalue
%o A105286     return filter(lambda k: not (prime(k+1)-1)%k,count(max(startvalue,1)))
%o A105286 A105286_list = list(islice(A105286_gen(),10)) # _Chai Wah Wu_, Dec 14 2022
%Y A105286 Cf. A004649, A105287, A105288, A105290, A105329, A105451.
%K A105286 nonn
%O A105286 1,2
%A A105286 _Zak Seidov_, Apr 25 2005
%E A105286 More terms from _Farideh Firoozbakht_, May 12 2005
%E A105286 First term inserted by _Eric M. Schmidt_, Feb 05 2013
%E A105286 More terms from _Michel Marcus_, Dec 29 2022
%E A105286 a(40)-a(47) from _Max Alekseyev_, Aug 31 2024