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

Author

Paul Tek, Nov 12 2013

Keywords

• nonn
• base

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

Examples

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

Links

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

Crossrefs

Cf. A135643, A231588.

Programs

Mathematica

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

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