A345352 -id:A345352 - cp's OEIS frontend

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

Rémy Sigrist, Jun 16 2021

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.

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

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

Cf. A001196, A057890, A345352.

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.
```

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

cp's OEIS Frontend

A345362 Fixed points of A345352.

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