A368866 The smallest positive number such that 2^a(n) when written in base n contains adjacent equal digits.

2, 2, 4, 5, 6, 3, 6, 12, 16, 14, 11, 15, 8, 4, 8, 23, 16, 14, 16, 21, 9, 17, 20, 14, 30, 27, 16, 15, 10, 5, 10, 29, 48, 14, 46, 19, 18, 15, 32, 36, 27, 36, 18, 12, 56, 41, 37, 24, 58, 22, 26, 46, 58, 40, 29, 24, 36, 14, 20, 18, 12, 6, 12, 60, 62, 50, 49, 50, 20, 35, 36, 55, 61, 52, 53, 77

Offset

2,1

Comments

In the first 10000 terms the largest value is a(9031) = 1924, with a corresponding power of 2 of approximately 1.52*10^579.

Links

Scott R. Shannon, Table of n, a(n) for n = 2..10000

Example

a(2) = 2 as 2^2 = 4 written in base 2 = 100_2 which contains adjacent 0's.
a(6) = 6 as 2^6 = 64 written in base 6 = 144_6 which contains adjacent 4's.
a(10) = 16 as 2^16 = 65536 written in base 10 = 65536_10 which contains adjacent 5's.

Maple

f:= proc(n) local k, L;
  for k from 1 do
    L:= convert(2^k, base, n);
    if member(0, L[2..-1]-L[1..-2]) then return k fi
  od
end proc:
map(f, [$2..100]); # Robert Israel, Jan 09 2024

Prog

(Python)
from itertools import count
from sympy.ntheory.factor_ import digits
def A368866(n):
    k = 1
    for m in count(1):
        k <<= 1
        s = digits(k, n)[1:]
        if any(s[i]==s[i+1] for i in range(len(s)-1)):
            return m # Chai Wah Wu, Jan 08 2024

Crossrefs

Cf. A000079, A171901, A011557, A004642, A004643, A000866.

Sequence in context: A121600 A126870 A364049 * A137413 A010848 A133937

Adjacent sequences: A368863 A368864 A368865 * A368867 A368868 A368869

Keyword

nonn,base

Author

Scott R. Shannon, Jan 08 2024

Status

approved