A274612 Numbers not divisible by 10 with at least one zero but no two adjacent 0's among its decimal digits.

101, 102, 103, 104, 105, 106, 107, 108, 109, 201, 202, 203, 204, 205, 206, 207, 208, 209, 301, 302, 303, 304, 305, 306, 307, 308, 309, 401, 402, 403, 404, 405, 406, 407, 408, 409, 501, 502, 503, 504, 505, 506, 507, 508, 509, 601, 602, 603, 604, 605, 606, 607, 608, 609, 701, 702, 703, 704, 705, 706, 707, 708, 709, 801, 802, 803, 804, 805, 806, 807, 808, 809, 901, 902, 903, 904, 905, 906, 907, 908, 909, 1011

Offset: 1

Author

José de Jesús Camacho Medina, Jun 30 2016

Keywords

• base
• easy
• nonn
• less

Examples

			101 is a term because 101 = 101  + (1^0 * 0^1);
1010 is a term because 1010 = 1010 + (1^0 * 0^1 * 1^0 ).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A134808, A005188.

Programs

Maple

filter:= proc(n) local L;
  L:= [ListTools:-SearchAll(0,convert(n,base,10))];
  nops(L) >= 1 and L[1]<>1 and not has(L[2..-1]-L[1..-2],1)
end proc:
select(filter, [$1..10000]); # Robert Israel, Jul 24 2016

Mathematica

AA = Table[(Product[(Mod[(Floor[f/10^n]), 10])^(Mod[(Floor[f/10^(n - 1)]), 10]), {n, 1, Floor[Log[10, f]]}]), {f, 1, 1200}]
BB = Table[n, {n, 1, 1200}]
Position[(AA + BB) - BB, 0]

PARI

is(n)=n%10 && vecmin(digits(n))==0 && vecmin(digits(n,100)) && vecmin(digits(n\10,100)) \\ Charles R Greathouse IV, Jul 18 2016