A131552 Least positive power of 3 having exactly n consecutive 1's in its decimal representation.

4, 19, 93, 334, 841, 3404, 7271, 7720, 44152, 406774, 993948, 2421339, 8786439, 11387707, 93548200

Offset

1,1

Comments

No more terms < 10^8. - Bert Dobbelaere, Mar 20 2019

Links

Table of n, a(n) for n=1..15.

Example

a(3)=93 because 3^93 (i.e., 235655016338368235499067731945871638181119123) is the smallest power of 3 to contain a run of 3 consecutive ones in its decimal form.

Mathematica

a = ""; Do[ a = StringJoin[a, "1"]; b = StringJoin[a, "1"]; k = 1; While[ StringPosition[ ToString[3^k], a] == {} || StringPosition[ ToString[3^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

Prog

(Python)
def A131552(n):
....m, s = 1, '1'*n
....for i in range(1, 10**9):
........m *= 3
........if s in str(m):
............return i
....return "search limit reached." # Chai Wah Wu, Dec 11 2014

Crossrefs

Cf. A195269, A131551, A131550, A131549, A131548, A131547, A131546, A131545, A131544.

Sequence in context: A181950 A288687 A275751 * A122369 A005978 A083065

Adjacent sequences: A131549 A131550 A131551 * A131553 A131554 A131555

Keyword

more,nonn,base

Author

Shyam Sunder Gupta, Aug 26 2007

Extensions

a(11)-a(14) from Lars Blomberg, Feb 02 2013

Definition edited by Chai Wah Wu, Dec 11 2014

a(15) from Bert Dobbelaere, Mar 20 2019

Status

approved