A034054 Numbers with multiplicative digital root value 7.

7, 17, 71, 117, 171, 711, 1117, 1171, 1711, 7111, 11117, 11171, 11711, 17111, 71111, 111117, 111171, 111711, 117111, 171111, 711111, 1111117, 1111171, 1111711, 1117111, 1171111, 1711111, 7111111, 11111117, 11111171, 11111711, 11117111

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base
• easy

Comments

Numbers with one 7, and zero or more 1s. - Daniel Forgues, Oct 09 2011

Links

• Eric Weisstein's World of Mathematics, Multiplicative Digital Root
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A031347.

Cf. A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 0-9).

Programs

Mathematica

Sort[Flatten[Table[FromDigits/@Permutations[Join[{7},PadRight[{},n,1]]],{n,0,10}]]] (* Harvey P. Dale, Jul 20 2015 *)

PARI

t(k)=while(k>9, k=prod(i=1, #k=digits(k), k[i])); k
for(n=1, 1e8, if(t(n) == 7, print1(n, ", "))); \\ Altug Alkan, Oct 22 2015

Formula

There are n(n+1)/2 elements up to 10^n, so a(n) is about 10^sqrt(2n).