A051813 -id:A051813 - cp's OEIS frontend

A263477 Total number of n-digit positive integers with multiplicative digital root value 2.

1, 8, 68, 466, 2670, 13460, 69420, 417722, 3025242, 21873040, 136901413, 722201372, 3271729383, 13114173697, 48104723380, 167526488628, 574289772576, 1988721563904, 7000834741144, 24759698208450, 86342520209963, 292206955736762, 950480594161453

Offset: 1

Martin Renner, Oct 19 2015

First differences of A263471.

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50
Eric Weisstein's World of Mathematics, Multiplicative Digital Root

Cf. A031347, A034049, A051813, A263471.

Last /@ Tally@ IntegerLength@ Select[Range@ 1000000, FixedPoint[Times @@ IntegerDigits@ # &, #] == 2 &] (* Michael De Vlieger, Oct 21 2015 *)

t(k) = {while(k>9, k=prod(i=1, #k=digits(k), k[i])); k}
a(n) = sum(i=10^(n-1), 10^n - 1, if(t(i) == 2, 1, 0)); \\ Altug Alkan, Oct 19 2015

A263476(n) + A000012(n) + a(n) + A000027(n) + A263478(n) + A263479(n) + A263480(n) + A000027(n) + A263481(n) + A000217(n) = A052268(n).

a(9)-a(23) from Hiroaki Yamanouchi, Oct 25 2015

A051822 Number of numbers below 10^n with nonzero multiplicative digital root 2.

Original entry on oeis.org

1, 16, 224, 2613, 27458, 271155, 2620040, 25457267, 251964768, 2537869322, 25777827199, 261509437991, 2634407279895, 26321038031960, 261379965909359, 2589357329707966

Offset: 1

Dan Hoey, Dec 09 1999

William Mayne, sci.math, Jun 15 1991

Cf. A051802, A051804, A051813.

# { i : 10^(n-1) < i < 10^n and A051802(i)=2 }

cp's OEIS Frontend

A263477 Total number of n-digit positive integers with multiplicative digital root value 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions