cp's OEIS Frontend

A349321 Numbers k such that k-1, k+1, 2k-1, 2k+1, 3k-1, 3k+1, 4k-1, 4k+1, 5k-1, and 5k+1 are all primes.

%I A349321 #15 Mar 21 2022 08:09:37
%S A349321 100803789240,441913177860,1768738337520,3906037699410,5988326187690,
%T A349321 6266477200830,6905441609220,6973884137220,14323608903450,
%U A349321 17683172090430,20047266723330,23371434572640,27904703386560,29484744885750,31141493827290,33202639844220,34645262968470
%N A349321 Numbers k such that k-1, k+1, 2k-1, 2k+1, 3k-1, 3k+1, 4k-1, 4k+1, 5k-1, and 5k+1 are all primes.
%C A349321 All terms are multiples of 2*3*5*7*11 = 2310.
%C A349321 From _Jon E. Schoenfield_, Mar 21 2022: (Start)
%C A349321 Each term is congruent to one of only
%C A349321        1 residue  modulo 2*3*5*7*11     =         2310 (0.04329%),
%C A349321        3 residues modulo 2*3*5*7*11*13  =        30030 (0.00999%),
%C A349321       21 residues modulo 2*3*5*7*...*17 =       510510 (0.00411%),
%C A349321      189 residues modulo 2*3*5*7*...*19 =      9699690 (0.00195%),
%C A349321     2457 residues modulo 2*3*5*7*...*23 =    223092870 (0.00110%),
%C A349321    46683 residues modulo 2*3*5*7*...*29 =   6469693230 (0.00072%),
%C A349321   980343 residues modulo 2*3*5*7*...*31 = 200560490130 (0.00049%), etc.;
%C A349321 making use of these can allow more efficient searching for terms of the sequence.
%C A349321 The Magma program (see Links) generates a list of the possible residues modulo 2*3*5*7*...*31 and tests only numbers having one of those residues. (Note that the program, when run on the Online Magma Calculator, generates only the first three terms of the sequence before being terminated on reaching the 120-second time limit.) (End)
%H A349321 Jon E. Schoenfield, <a href="/A349321/a349321.txt">Magma program</a>
%o A349321 (PARI) is_ok(k)=for(j=1,5, if(!isprime(j*k-1), return(0)); if(!isprime(j*k+1), return(0));); return(1); \\ _Joerg Arndt_, Nov 15 2021
%Y A349321 Cf. A014574, A066388, A118859, A118860, A348348.
%K A349321 nonn
%O A349321 1,1
%A A349321 _Jon E. Schoenfield_, Nov 14 2021