A131546 Least power of 3 having exactly n consecutive 7's in its decimal representation.

3, 11, 112, 184, 721, 3520, 6643, 12793, 67448, 208380, 364578, 1123485, 9549790, 23340555, 88637856

Offset: 1

Author

Shyam Sunder Gupta, Aug 26 2007

Keywords

• more
• nonn
• base

Comments

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

Examples

			a(2) = 11 because 3^11 = 177147 is the smallest power of 3 to contain a run of two consecutive 7's in its decimal form.
		

Crossrefs

Cf. A195269, A131552, A131551, A131550, A131549, A131548, A131547, A131545, A131544.

Programs

Mathematica

a = ""; Do[ a = StringJoin[a, "7"]; b = StringJoin[a, "7"]; k = 1; While[ StringPosition[ ToString[3^k], a] == {} || StringPosition[ ToString[3^k], b] != {}, k++ ]; Print[k], {n, 10} ]

Python

import sys
sys.set_int_max_str_digits(1000000)
def A131546(n):
    str7 = '7'*n
    x, exponent = 3, 1
    while not str7 in str(x):
        exponent += 1
        x *= 3
    return exponent # Chai Wah Wu, Aug 05 2014

Formula

a(1) = A063566(7). - Michel Marcus, Aug 05 2014

Extensions

a(11)-a(13) from Lars Blomberg, Feb 02 2013

a(14)-a(15) from Bert Dobbelaere, Mar 20 2019