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

1,1

Comments

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

Links

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Multiplicative Digital Root

Index entries for 10-automatic sequences.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A031347.

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

Sequence in context: A051809 A254500 A242907 * A120876 A216073 A086870

Adjacent sequences: A034051 A034052 A034053 * A034055 A034056 A034057

Keyword

nonn,base,easy

Author

Patrick De Geest, Sep 15 1998

Status

approved