A231588 Primes with decimal digits in arithmetic progression mod 10.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 109, 173, 197, 307, 383, 593, 727, 739, 937, 2963, 4567, 4703, 5791, 7159, 8147, 9371, 10987, 15937, 19753, 37159, 52963, 53197, 58147, 71593, 72727, 73951, 76543

Offset: 1

Author

Paul Tek, Nov 11 2013

Keywords

• base
• nonn

Comments

This sequence contains straight-line primes (A167847).

a(216) has 1012 digits. - Michael S. Branicky, Aug 05 2022

Examples

			(7,2,7,2,7,...) is an arithmetic progression mod 10, hence the prime number 72727 appears in this sequence.
(7,6,5,4,3,...) is an arithmetic progression mod 10, hence the prime number 76543 appears in this sequence.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..215 (terms 1..147 from Paul Tek)
• Paul Tek, PARI program for this sequence

Crossrefs

Cf. A167847.

Programs

Mathematica

Select[Prime[Range[PrimePi[76543]]], Length[Union[Mod[Differences[IntegerDigits[#]], 10]]] <= 1 &]

PARI

See Link section.

Python

from sympy import isprime
from itertools import count, islice
def bgen():
    yield from [2, 3, 5, 7]
    yield from (int("".join(str((s0+i*r)%10) for i in range(d))) for d in count(2) for s0 in range(1, 10) for r in range(-s0, 10-s0))
def agen(): yield from filter(isprime, bgen())
print(list(islice(agen(), 52))) # Michael S. Branicky, Aug 05 2022