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

1, 10, 11, 21, 31, 41, 51, 61, 71, 81, 91, 100, 101, 110, 111, 121, 131, 141, 151, 161, 171, 181, 191, 201, 210, 211, 221, 231, 241, 251, 261, 271, 281, 291, 301, 310, 311, 321, 331, 341, 351, 361, 371, 381, 391, 401, 410, 411, 421, 431, 441, 451, 461, 471

Offset: 1

Author

Clark Kimberling, Nov 05 2016

Keywords

• nonn
• easy
• base

Comments

Positions of 1 in A065881.

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.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A277589-A277596.

Programs

Maple

M:= 4: # to get all terms with <= M digits
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

Mathematica

z = 460; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[10, 1] (* A277588 *)
p[10, 2] (* A277589 *)
p[10, 3] (* A277590 *)
p[10, 4] (* A277591 *)
p[10, 5] (* A277592 *)
p[10, 6] (* A277593 *)
p[10, 7] (* A277594 *)
p[10, 8] (* A277595 *)
p[10, 9] (* A277596 *)
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 *)

PARI

is(n)=n && n/10^valuation(n,10)%10==1 \\ Charles R Greathouse IV, Jan 31 2017