A052057
Numbers k such that the decimal expansion of 2^k contains no palindromic substring except single digits.
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 29, 37, 54
Offset: 1
Record number is 2^54 = 18014398509481984.
A052059
Least k such that the longest palindromic substring (without leading zeros) contained in 2^k has length n.
Original entry on oeis.org
0, 16, 17, 47, 49, 41, 146, 274, 76, 468, 1622, 4381, 2961, 12799, 4292, 28493, 34597, 16276
Offset: 1
a(3) = 17 since 2^17 = {131}072.
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def ispal(s): return s == s[::-1]
def longestpalss(n):
s = str(n)
for l in range(len(s), 0, -1):
for offset in range(len(s)-l+1):
if s[offset] != '0' and ispal(s[offset:offset+l]):
return l
def a(n):
k, pow2 = 0, 1
while longestpalss(pow2) != n: k += 1; pow2 <<= 1
return k
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Nov 12 2021
Title clarified, a(11) corrected, and a(12)-a(15) from
Sean A. Irvine, Oct 19 2021
Showing 1-2 of 2 results.
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