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

%I A231701 #21 Aug 05 2022 15:48:22
%S A231701 109,111,123,135,147,159,161,173,185,197,208,210,222,234,246,258,260,
%T A231701 272,284,296,307,319,321,333,345,357,369,371,383,395,406,418,420,432,
%U A231701 444,456,468,470,482,494,505,517,529,531,543,555,567,579,581,593,604,616
%N A231701 Numbers > 100 with decimal digits in arithmetic progression mod 10.
%C A231701 This sequence contains straight-line numbers > 99 (A135643).
%C A231701 Each set of numbers from 10^n to 10^(n+1) contains 90 of these numbers. - _T. D. Noe_, Nov 12 2013
%C A231701 The sequence mod 100 has period 900, the sequence mod 90 has period 8100. - _Paul Tek_, Nov 14 2013
%H A231701 Michael S. Branicky, <a href="/A231701/b231701.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Paul Tek)
%e A231701 (8,2,6,0,4,...) is an arithmetic progression mod 10, hence the number 82604 appears in this sequence.
%t A231701 Select[Range[100, 10^3], Length[Union[Mod[Differences[IntegerDigits[#]], 10]]] <= 1 &] (* _T. D. Noe_, Nov 12 2013 *)
%o A231701 (PARI) a(n) = my(len=3+(n-1)\90,   \
%o A231701                  fs=10+((n-1)%90), \
%o A231701                  f=fs\10,          \
%o A231701                  s=fs%10);         \
%o A231701                return(sum(i=1,len,10^(len-i)*((f+(i-1)*(s-f))%10)))
%o A231701 (Python)
%o A231701 from itertools import count, islice
%o A231701 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))
%o A231701 print(list(islice(agen(), 52))) # _Michael S. Branicky_, Aug 05 2022
%Y A231701 Cf. A135643, A231588.
%K A231701 nonn,base
%O A231701 1,1
%A A231701 _Paul Tek_, Nov 12 2013