A161978 a(n) = the smallest positive integer that when written in binary contains both binary n and {the string formed from the reversal of the binary digits of n, with leading 0's removed} as (possibly overlapping) substrings.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 27, 12, 27, 14, 15, 16, 17, 18, 51, 20, 21, 45, 93, 24, 51, 90, 27, 28, 93, 30, 31, 32, 33, 34, 99, 36, 165, 102, 231, 40, 165, 42, 107, 108, 45, 93, 189, 48, 99, 306, 51, 180, 107, 54, 119, 56, 231, 186, 119, 60, 189, 62, 63, 64, 65, 66, 195

Offset

1,2

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..5000

Example

22 in binary is 10110. The binary string with the smallest numerical value that contains both 10110 and its reversal (with the leading 0 removed), 1101, is 101101. a(22) is the numerical value (written in decimal) of this binary string, which is 45.

Prog

(Python)
def A161978(n):
    b, i = bin(n)[2:], -1
    r = b[::-1]
    s = r.index('1')
    while n:
        i += 1
        k = bin(n+i)[2:]
        if k.find(b) != -1:
            if k.find(r[s:]) != -1: break
    return n+i # John Tyler Rascoe, Mar 11 2023

Crossrefs

Cf. A030101.

Sequence in context: A095205 A344325 A366389 * A132579 A004850 A260096

Adjacent sequences: A161975 A161976 A161977 * A161979 A161980 A161981

Keyword

base,look,nonn

Author

Leroy Quet, Jun 23 2009

Extensions

Corrected and extended by Sean A. Irvine, Nov 09 2009

Status

approved