A162742 -id:A162742 - cp's OEIS frontend

A376857 Fixed points of A162742.

1, 3, 5, 7, 9, 15, 17, 21, 25, 27, 31, 35, 45, 49, 51, 63, 73, 75, 81, 85, 93, 105, 107, 119, 125, 127, 135, 143, 147, 153, 155, 175, 189, 217, 219, 225, 243, 245, 255, 257, 279, 289, 313, 315, 321, 343, 357, 365, 375, 381, 405, 425, 429, 441, 443, 459, 465, 511, 525, 527, 535

Offset: 1

Paolo Xausa, Oct 07 2024

First differs from A342572 at n = 28. In the present sequence a(28) = 143 = 11 * 13: 11 and 13 are the binary reversals of each other but neither is a binary palindrome, so 143 is not in A342572.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A162742. Supersequence of A342572.

A376857Q[k_] := k == Times @@ (IntegerReverse[#1, 2]^#2 & @@@ FactorInteger[k]);
Select[Range[1000], A376857Q]

# uses function, imports in A162742
def ok(n): return n > 0 and n == A162742(n)
print([k for k in range(536) if ok(k)]) # Michael S. Branicky, Oct 07 2024

A161955 TITO2(n): The operation A161594 in binary, digit-reversals carried out in base 2.

Original entry on oeis.org

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 19, 13, 27, 7, 29, 15, 31, 1, 57, 17, 49, 9, 37, 19, 33, 5, 41, 21, 43, 11, 45, 23, 47, 3, 35, 19, 51, 13, 53, 27, 65, 7, 105, 29, 59, 15, 61, 31, 63, 1, 59, 57, 67, 17, 117, 49, 71, 9, 73, 37, 105, 19, 109

Offset: 1

Tanya Khovanova, Jun 22 2009

The TITO function in binary: Represent n as a product of its prime factors in binary.

Revert the binary digits of each of these factors, then multiply them with the same multiplicities as in n--so the base-2 representation does not affect the exponents in the canonical prime factorization. Reverse the product in binary to get a(n).

			To calculate TITO2(n=99): 99 = 3^3*11. Prime factors 3 and 11 in binary are 11 and 1011 correspondingly. Reversing those numbers we get 11 and 1101. The product with multiplicities is the binary product of 11*11*1101 = 1110101. Reversing that we get 1010111, which corresponds to 87. Hence a(99) = 87.

Alois P. Heinz, Table of n, a(n) for n = 1..40000
Tanya Khovanova, Turning Numbers Inside Out

Cf. A161594.

r:= proc(n) local m, t; m, t:=n, 0; while m>0
      do t:=2*t+irem(m, 2, 'm') od; t end:
a:= n-> r(mul(r(i[1])^i[2], i=ifactors(n)[2])):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 29 2017

reverseBinPower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n, 2]], 2]^k fBin[n_] := FromDigits[ Reverse[IntegerDigits[ Times @@ Map[reverseBinPower, FactorInteger[n]], 2]], 2] Table[fBin[n], {n, 200}]

a(n) = A030101(A162742(n)) - R. J. Mathar, Aug 03 2009

Edited by R. J. Mathar, Aug 03 2009

cp's OEIS Frontend

A376857 Fixed points of A162742.

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A161955 TITO2(n): The operation A161594 in binary, digit-reversals carried out in base 2.

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