A131537 Least exponent k such that 2^k has exactly n consecutive 3's in its decimal representation.

5, 25, 83, 219, 221, 2270, 11020, 18843, 192915, 271978, 743748, 1039315, 13873203, 14060685

Offset

1,1

Comments

No more terms < 28*10^6.

Links

Table of n, a(n) for n=1..14.

Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16.

Example

a(3) = 83 because 2^83 (= 9671406556917033397649408) is the smallest power of 2 to contain a run of exactly 3 consecutive threes in its decimal form.

Mathematica

a = ""; Do[ a = StringJoin[a, "3"]; b = StringJoin[a, "3"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 9} ]

Prog

(Python)
def a(n):
  k, n2, np2 = 1, '3'*n, '3'*(n+1)
  while True:
    while not n2 in str(2**k): k += 1
    if np2 not in str(2**k): return k
    k += 1
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, May 25 2021

Crossrefs

Cf. A000079.

Sequence in context: A355949 A147114 A296669 * A250555 A147122 A051229

Adjacent sequences: A131534 A131535 A131536 * A131538 A131539 A131540

Keyword

nonn,base,more

Author

Shyam Sunder Gupta, Aug 26 2007

Extensions

a(10)-a(12) from Sean A. Irvine, Jul 19 2010

a(13)-a(14) from Lars Blomberg, Jan 24 2013

Status

approved