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A277588 Numbers k such that k/10^m == 1 mod 10, where 10^m is the greatest power of 10 that divides n.

%I A277588 #14 Jan 31 2017 01:00:39
%S A277588 1,10,11,21,31,41,51,61,71,81,91,100,101,110,111,121,131,141,151,161,
%T A277588 171,181,191,201,210,211,221,231,241,251,261,271,281,291,301,310,311,
%U A277588 321,331,341,351,361,371,381,391,401,410,411,421,431,441,451,461,471
%N A277588 Numbers k such that k/10^m == 1 mod 10, where 10^m is the greatest power of 10 that divides n.
%C A277588 Positions of 1 in A065881.
%C A277588 Numbers having 1 as rightmost nonzero digit in base 10. This is one sequence in a 10-way splitting of the positive integers; the other nine are indicated in the Mathematica program.
%H A277588 Clark Kimberling, <a href="/A277588/b277588.txt">Table of n, a(n) for n = 1..10000</a>
%p A277588 M:= 4: # to get all terms with <= M digits
%p A277588 A:= sort([seq(seq(10^d*(10*x+1),x=0..10^(M-1-d)-1),d=0..M-2)]); # _Robert Israel_, Nov 07 2016
%t A277588 z = 460; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
%t A277588 p[b_, d_] := Flatten[Position[a[b], d]]
%t A277588 p[10, 1] (* A277588 *)
%t A277588 p[10, 2] (* A277589 *)
%t A277588 p[10, 3] (* A277590 *)
%t A277588 p[10, 4] (* A277591 *)
%t A277588 p[10, 5] (* A277592 *)
%t A277588 p[10, 6] (* A277593 *)
%t A277588 p[10, 7] (* A277594 *)
%t A277588 p[10, 8] (* A277595 *)
%t A277588 p[10, 9] (* A277596 *)
%t A277588 f[n_] := Block[{m = n}, While[ Mod[m, 10] == 0, m /= 10]; Mod[m, 10]]; Flatten@ Position[ Array[f, 500], 1] (* _Robert G. Wilson v_, Nov 06 2016 *)
%o A277588 (PARI) is(n)=n && n/10^valuation(n,10)%10==1 \\ _Charles R Greathouse IV_, Jan 31 2017
%Y A277588 Cf. A277589-A277596.
%K A277588 nonn,easy,base
%O A277588 1,2
%A A277588 _Clark Kimberling_, Nov 05 2016