cp's OEIS Frontend

A105288 Numbers k such that prime(k+1) == 3 (mod k).

%I A105288 #33 Aug 02 2025 06:30:01
%S A105288 1,2,4,5,70,440,1055,1058,6461,6466,6469,251752,4124468,27067036,
%T A105288 27067112,69709709,69709957,465769835,8179002104,145935689357,
%U A105288 382465573490
%N A105288 Numbers k such that prime(k+1) == 3 (mod k).
%C A105288 Integers k such that A004649(k+1) = 3. - _Michel Marcus_, Dec 30 2022
%p A105288 n:= 0: p:= 2: count:= 0:
%p A105288 for n from 1 while count < 13 do
%p A105288 p:= nextprime(p);
%p A105288 if p-3 mod n = 0 then
%p A105288     count:= count+1;
%p A105288   A[count]:= n;
%p A105288   fi
%p A105288 od:
%p A105288 seq(A[i],i=1..count); # _Robert Israel_, May 02 2018
%t A105288 bb={};Do[If[3==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 200000}];bb
%t A105288 Join[{1, 2}, Select[Range[2 10^7], Mod[Prime[# + 1], #]==3 &]] (* _Vincenzo Librandi_, May 02 2018 *)
%o A105288 (Sage)
%o A105288 def A105288(max) :
%o A105288     terms = []
%o A105288     p = 3
%o A105288     for n in range(1, max+1) :
%o A105288         if (p - 3) % n == 0 : terms.append(n)
%o A105288         p = next_prime(p)
%o A105288     return terms
%o A105288 # _Eric M. Schmidt_, Feb 05 2013
%o A105288 (Magma) [1,2] cat [n: n in [1..2*10^4] | NthPrime(n+1) mod n eq 3]; // _Vincenzo Librandi_, May 02 2018
%Y A105288 Cf. A004649, A105286, A105287, A105290, A105329, A105451.
%K A105288 nonn,more
%O A105288 1,2
%A A105288 _Zak Seidov_, Apr 25 2005
%E A105288 First two terms inserted by _Eric M. Schmidt_, Feb 05 2013
%E A105288 a(12)-a(13) from _Robert Israel_, May 02 2018
%E A105288 a(14)-a(21) from _Giovanni Resta_, May 02 2018