A263479 Total number of n-digit positive integers with multiplicative digital root value 5.

1, 6, 33, 132, 435, 1466, 5341, 18656, 58029, 159430, 392601, 882036, 1836159, 3586506, 6638885, 11738656, 19952441, 32768742, 52220113, 81029700, 122785131, 182142906, 265066605, 379102400, 533695525, 740551526, 1014046281, 1371688948, 1834642167, 2428304010

Offset

1,2

Comments

First differences of A263473.

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

A263476(n) + A000012(n) + A263477(n) + A000027(n) + A263478(n) + a(n) + A263480(n) + A000027(n) + A263481(n) + A000217(n) = A052268(n).

a(n) = (1/720)*(3*n^8 + 6*n^7 - 664*n^6 + 6270*n^5 - 25783*n^4 + 55164*n^3 - 57796*n^2 + 23520*n). - Sergio Pimentel, Mar 27 2024

From Chai Wah Wu, Apr 17 2024: (Start)

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n > 9.

G.f.: x*(235*x^7 - 205*x^6 - 161*x^5 - 57*x^4 + 33*x^3 - 15*x^2 + 3*x - 1)/(x - 1)^9. (End)

Mathematica

Last /@ Tally@ IntegerLength@ Select[Range@ 1000000, FixedPoint[Times @@ IntegerDigits@ # &, #] == 5 &] (* Michael De Vlieger, Oct 21 2015 *)

Prog

(PARI) 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) == 5, 1, 0)); \\ Altug Alkan, Oct 19 2015

Crossrefs

Cf. A031347, A034052, A263473.

Sequence in context: A063267 A082106 A297392 * A073375 A089097 A120009

Adjacent sequences: A263476 A263477 A263478 * A263480 A263481 A263482

Keyword

nonn,base,changed

Author

Martin Renner, Oct 19 2015

Extensions

a(9)-a(30) from Hiroaki Yamanouchi, Oct 25 2015

Status

approved