A345362 Fixed points of A345352.

0, 1, 2, 3, 12, 15, 96, 102, 105, 111, 144, 150, 153, 159, 240, 246, 249, 255, 6144, 6168, 6180, 6204, 6210, 6234, 6246, 6270, 6273, 6297, 6309, 6333, 6339, 6363, 6375, 6399, 9216, 9240, 9252, 9276, 9282, 9306, 9318, 9342, 9345, 9369, 9381, 9405, 9411, 9435

Offset: 1

Author

Rémy Sigrist, Jun 16 2021

Keywords

• nonn
• base

Comments

The binary expansion of a term > 1 can be split into two symmetrical parts of the same size (this size being a power of 2) (possibly after adjoining some leading 0's), and the first part contains at least one 1.

If m is a term, then A001196(m) is also a term.

Examples

			A345352(96) = 96, so 96 belongs to this sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n
• Rémy Sigrist, Binary plot of the terms < 2^16
• Rémy Sigrist, PARI program for A345362

Crossrefs

Cf. A001196, A057890, A345352.

Programs

PARI

is(n) = { my (b=binary(n), x); for (k=1, oo, x=2^k-#b; if (x>=0, b=concat(vector(x), b); return (n==fromdigits(concat(Vecrev(b[1..#b/2]), Vecrev(b[#b/2+1..#b])), 2)))) }

PARI

See Links section.

Python

def A345352(n):
    b = bin(n)[2:]
    bb = bin(len(b))[2:]
    if bb != '1' + '0'*(len(bb)-1): b = '0'*(2**len(bb) - len(b)) + b
    return int(b[:len(b)//2][::-1] + b[len(b)//2:][::-1], 2)
def ok(n): return A345352(n) == n
print(list(filter(ok, range(9436))))  # Michael S. Branicky, Jun 16 2021