A088253 Smallest prime whose digits can be partitioned into n successive terms of an A.P. with common difference n, or 0 if no such number exists.

2, 13, 0, 15913, 38131823, 0, 55626976839097, 715233139475563, 0, 2939495969798999109119, 1324354657687990101112123, 0, 4760738699112125138151164177190203, 617589103117131145159173187201215229243, 0, 2339557187103119135151167183199215231247263

Offset

1,1

Comments

a(211) has 1008 digits. - Michael S. Branicky, Jun 23 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..210

Formula

a(3*k) = 0. - Michael S. Branicky, Jun 23 2023

Example

The terms of the A.P. in triangular form
  2
  1   3
  0   0   0
  1   5   9  13
  3   8  13  18  23
  0   0   0   0   0   0
  ...
Sequence contains the primes arising as a concatenation of the terms of the n-th row.

Prog

(Python)
from gmpy2 import is_prime
from itertools import count
def a(n): return next(t for t in (int("".join(str(i) for i in range(k, k+n*n, n))) for k in count(1)) if is_prime(t)) if n%3 else 0
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Jun 23 2023

Crossrefs

Sequence in context: A128033 A090954 A089778 * A249224 A217010 A091023

Adjacent sequences: A088250 A088251 A088252 * A088254 A088255 A088256

Keyword

base,nonn

Author

Amarnath Murthy, Sep 26 2003

Extensions

a(7)-a(10) from Charlie Neder, May 12 2019

a(11) and beyond from Michael S. Branicky, Jun 23 2023

Status

approved