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

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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(PARI) 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)))
(Python)
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

Crossrefs

Cf. A135643, A231588.

Sequence in context: A253431 A253438 A263194 * A051046 A196667 A196673

Adjacent sequences: A231698 A231699 A231700 * A231702 A231703 A231704

Keyword

nonn,base

Author

Paul Tek, Nov 12 2013

Status

approved