A350679 Irregular triangle read by rows: T(n,k) (n>=0) is the least prime such that T(n,k) + r*i (0 <= i < k) is an arithmetic progression of primes with first difference primorial(n), or 0 if no such prime exists.

2, 2, 2, 3, 3, 2, 5, 5, 5, 5, 2, 7, 7, 7, 7, 7, 0, 2, 13, 13, 13, 13, 13, 47, 199, 199, 199, 0, 2, 23, 23, 29, 37, 37, 71, 1019, 3823, 2564251, 60858179, 147692845283, 0, 2, 17, 17, 17, 73, 73, 619, 4657, 4657, 6007, 23143, 23143, 14933623, 834172298383, 894476585908771, 1275290173428391, 0

Offset

0,1

Links

Table of n, a(n) for n=0..57.

Jens Kruse Andersen, Records for primes in arithmetic progressions

Example

T(4,7)=47 because the primes 47 + r*i (0 <= i < 7) with r = primorial(4) = 2*3*5*7 = 210 are in arithmetic progression.
Triangle begins
  2,  2;
  2,  3,  3;
  2,  5,  5,  5,  5;
  2,  7,  7,  7,  7,  7,  0;
  2, 13, 13, 13, 13, 13, 47, 199, 199, 199, 0;
  ...

Mathematica

Flatten@Table[Join[Table[j=1; While[k=1; While[PrimeQ[Prime@j+ k(r=Times@@Prime@Range@n)], k++]; k<m, j++]; (p=Prime@j), {m, Prime[n+1]-1}], {If[And@@Table[PrimeQ[p+k*r], {k, 0, p-1}], p, 0]}], {n, 0, 4}] (* Giorgos Kalogeropoulos, Jan 12 2022 *)

Crossrefs

Cf. A002110.

Sequence in context: A194332 A322062 A368460 * A071451 A177868 A178701

Adjacent sequences: A350676 A350677 A350678 * A350680 A350681 A350682

Keyword

nonn,tabf

Author

Jean-Marc Rebert, Jan 11 2022

Status

approved