A046260 -id:A046260 - 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 *)

A046268 Largest prime substring in 2^n (or 0 if none exist).

Original entry on oeis.org

0, 2, 0, 0, 0, 3, 0, 2, 5, 5, 2, 2, 409, 19, 163, 7, 6553, 131, 2621, 5, 857, 971, 419, 83, 1677721, 5443, 71, 1342177, 43, 709, 107, 83, 4294967, 89, 171798691, 3597383, 6871947673, 3743895347, 779069, 54975581, 511627, 99023, 4398046511, 79609, 18604441, 883

Offset: 0

Patrick De Geest, Jun 15 1998

nonn

			2^37 = 1{3743895347}2, so a(37) = 3743895347.

Michael S. Branicky, Table of n, a(n) for n = 0..2000

Cf. A000079, A046260, A047814.

from sympy import isprime
def a(n):
    s = str(2**n)
    ss = (int(s[i:j]) for i in range(len(s)) for j in range(i+1, len(s)+1))
    return max((k for k in ss if isprime(k)), default=0)
print([a(n) for n in range(46)]) # Michael S. Branicky, Sep 20 2022

a(n) = A047814(2^n). - Pontus von Brömssen, Jan 16 2025

a(44) and beyond from Michael S. Branicky, Sep 20 2022

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

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A046268 Largest prime substring in 2^n (or 0 if none exist).

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