A046268 -id:A046268 - cp's OEIS frontend

A050723 Numbers k such that the decimal expansion of 2^k contains no pair of consecutive equal digits (probably finite).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 20, 21, 22, 28, 29, 30, 31, 32, 34, 35, 36, 37, 48, 54, 55, 56, 66, 67, 68, 69, 80, 87, 104, 126

Offset: 1

Patrick De Geest, Sep 15 1999

No further terms up to 100000. - T. D. Noe, Sep 18 2012

			2^126 = 85070591730234615865843651857942052864.

Cf. A043096, A007377, A046260, A046268.

q:= n-> (s-> andmap(i-> s[i]<>s[i+1], [$1..length(s)-1]))(""||(2^n)):
select(q, [$0..200])[];  # Alois P. Heinz, Mar 07 2024

Select[Range[0,10000],!MemberQ[Differences[IntegerDigits[2^#]],0]&] (* Harvey P. Dale, Dec 24 2011 *)

A046260 Largest palindromic substring in 2^n.

Original entry on oeis.org

1, 2, 4, 8, 6, 3, 6, 8, 6, 5, 4, 8, 9, 9, 8, 8, 55, 131, 262, 242, 8, 9, 9, 838, 777, 55, 88, 77, 545, 9, 737, 474, 949, 858, 717, 383, 767, 9, 77, 888, 777, 255552, 111, 222, 444, 888, 77, 3553, 767, 21312, 42624, 99, 737, 474, 9, 797, 575, 8558, 7117, 646, 606, 939

Offset: 0

Patrick De Geest, Jun 15 1998

			2^41 = 2199023{255552}.

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Cf. A000079, A047813, A046268.

def c(s): return s[0] != "0" and s == s[::-1]
def a(n):
    s = str(2**n)
    ss = (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1))
    return max(int(w) for w in ss if c(w))
print([a(n) for n in range(62)]) # Michael S. Branicky, Sep 18 2022

a(n) = A047813(A000079(n)). - Michel Marcus, Sep 19 2022

cp's OEIS Frontend

A050723 Numbers k such that the decimal expansion of 2^k contains no pair of consecutive equal digits (probably finite).

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