A231588 -id:A231588 - cp's OEIS frontend

A232066 Periodic primes: primes p whose decimal expansion can be written as sss...st, where s is nonempty string of digits not beginning with 0, there are at least two copies of s, and t (which may be absent) is a prefix of s.

11, 18181, 32323, 35353, 72727, 74747, 78787, 94949, 95959, 1041041, 1051051, 1131131, 1191191, 1201201, 1212121, 1221221, 1231231, 1261261, 1281281, 1311311, 1381381, 1401401, 1411411, 1491491, 1501501, 1551551, 1581581, 1616161, 1621621, 1641641, 1671671

Offset: 1

Paul Tek, Nov 17 2013

The terms > 10^4 in A032758 appear in this sequence.

The terms > 10^20 in A231588 appear in this sequence.

			9779779 = 977|977|9,
727272727 = 72|72|72|72|7 = 7272|7272|7.

Paul Tek, Table of n, a(n) for n = 1..5972
Paul Tek, PARI program for this sequence

Cf. A032758, A231588.

A004022 is a subsequence (these are the terms where s=1 and t is absent). - Harvey P. Dale, Jul 09 2019

PARI
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Definition corrected by N. J. A. Sloane, Jul 09 2019

A231701 Numbers > 100 with decimal digits in arithmetic progression mod 10.

Original entry on oeis.org

109, 111, 123, 135, 147, 159, 161, 173, 185, 197, 208, 210, 222, 234, 246, 258, 260, 272, 284, 296, 307, 319, 321, 333, 345, 357, 369, 371, 383, 395, 406, 418, 420, 432, 444, 456, 468, 470, 482, 494, 505, 517, 529, 531, 543, 555, 567, 579, 581, 593, 604, 616

Offset: 1

Paul Tek, Nov 12 2013

This sequence contains straight-line numbers > 99 (A135643).
Each set of numbers from 10^n to 10^(n+1) contains 90 of these numbers. - T. D. Noe, Nov 12 2013
The sequence mod 100 has period 900, the sequence mod 90 has period 8100. - Paul Tek, Nov 14 2013

			(8,2,6,0,4,...) is an arithmetic progression mod 10, hence the number 82604 appears in this sequence.

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paul Tek)

Cf. A135643, A231588.

Select[Range[100, 10^3], Length[Union[Mod[Differences[IntegerDigits[#]], 10]]] <= 1 &] (* T. D. Noe, Nov 12 2013 *)

a(n) = my(len=3+(n-1)\90,   \
                 fs=10+((n-1)%90), \
                 f=fs\10,          \
                 s=fs%10);         \
               return(sum(i=1,len,10^(len-i)*((f+(i-1)*(s-f))%10)))

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

cp's OEIS Frontend

A232066 Periodic primes: primes p whose decimal expansion can be written as sss...st, where s is nonempty string of digits not beginning with 0, there are at least two copies of s, and t (which may be absent) is a prefix of s.

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