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 A274612 Numbers not divisible by 10 with at least one zero but no two adjacent 0's among its decimal digits. 1

%I #21 Apr 05 2020 22:27:39

%S 101,102,103,104,105,106,107,108,109,201,202,203,204,205,206,207,208,

%T 209,301,302,303,304,305,306,307,308,309,401,402,403,404,405,406,407,

%U 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

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

%H Robert Israel, <a href="/A274612/b274612.txt">Table of n, a(n) for n = 1..10000</a>

%e 101 is a term because 101 = 101 + (1^0 * 0^1);

%e 1010 is a term because 1010 = 1010 + (1^0 * 0^1 * 1^0 ).

%p filter:= proc(n) local L;

%p L:= [ListTools:-SearchAll(0,convert(n,base,10))];

%p nops(L) >= 1 and L[1]<>1 and not has(L[2..-1]-L[1..-2],1)

%p end proc:

%p select(filter, [\$1..10000]); # _Robert Israel_, Jul 24 2016

%t 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}]

%t BB = Table[n, {n, 1, 1200}]

%t Position[(AA + BB) - BB, 0]

%o (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

%Y Cf. A134808, A005188.

%K base,easy,nonn,less

%O 1,1

%A _José de Jesús Camacho Medina_, Jun 30 2016

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Last modified June 20 22:01 EDT 2024. Contains 373532 sequences. (Running on oeis4.)