A063629 Smallest k such that 9^k has exactly n 3's in its decimal representation.

1, 6, 11, 24, 30, 38, 33, 28, 55, 57, 53, 56, 84, 109, 86, 124, 145, 118, 126, 159, 134, 164, 161, 197, 155, 212, 246, 217, 222, 250, 249, 248, 294, 300, 293, 328, 274, 295, 298, 287, 289, 404, 385, 354, 361, 366, 412, 407, 359, 438, 417

Offset

0,2

Comments

What is the least n such that a(n) does not exist? Heuristics suggest around a(50000). - Charles R Greathouse IV, Dec 29 2014

The least n's such that a(n) does not exist appear to be 25337 and 89200, based on the computation of 9^k < 10^1450000. - Giovanni Resta, Jun 27 2018

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Mathematica

a = {}; Do[k = 1; While[ Count[ IntegerDigits[9^k], 3] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a
Module[{nn=50, k=9^Range[500]}, Table[Position[k, _?(DigitCount[#, 10, 3]==n&), 1, 1], {n, 0, nn}]]//Flatten (* Harvey P. Dale, Jun 30 2022 *)

Prog

(PARI) a(n)=my(k, d); while(1, d=digits(9^k); if(sum(i=1, #d, d[i]==3)==n, return(k)); k++) \\ Charles R Greathouse IV, Dec 29 2014

Crossrefs

Sequence in context: A309742 A362442 A372999 * A076496 A354594 A219628

Adjacent sequences: A063626 A063627 A063628 * A063630 A063631 A063632

Keyword

base,nonn

Author

Robert G. Wilson v, Aug 10 2001

Status

approved