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%I #29 Dec 30 2022 06:30:37
%S 1,2,4,5,70,440,1055,1058,6461,6466,6469,251752,4124468,27067036,
%T 27067112,69709709,69709957,465769835,8179002104,145935689357,
%U 382465573490
%N Numbers k such that prime(k+1) == 3 (mod k).
%C Integers k such that A004649(k+1) = 3. - _Michel Marcus_, Dec 30 2022
%p n:= 0: p:= 2: count:= 0:
%p for n from 1 while count < 13 do
%p p:= nextprime(p);
%p if p-3 mod n = 0 then
%p count:= count+1;
%p A[count]:= n;
%p fi
%p od:
%p seq(A[i],i=1..count); # _Robert Israel_, May 02 2018
%t bb={};Do[If[3==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 200000}];bb
%t Join[{1, 2}, Select[Range[2 10^7], Mod[Prime[# + 1], #]==3 &]] (* _Vincenzo Librandi_, May 02 2018 *)
%o (Sage)
%o def A105288(max) :
%o terms = []
%o p = 3
%o for n in range(1, max+1) :
%o if (p - 3) % n == 0 : terms.append(n)
%o p = next_prime(p)
%o return terms
%o # _Eric M. Schmidt_, Feb 05 2013
%o (Magma) [1,2] cat [n: n in [1..2*10^4] | NthPrime(n+1) mod n eq 3]; // _Vincenzo Librandi_, Maj 02 2018
%Y Cf. A004649, A105286, A105287, A105290, A105329, A105451.
%K nonn,more
%O 1,2
%A _Zak Seidov_, Apr 25 2005
%E First two terms inserted by _Eric M. Schmidt_, Feb 05 2013
%E a(12)-a(13) from _Robert Israel_, May 02 2018
%E a(14)-a(21) from _Giovanni Resta_, May 02 2018
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