A161603 -id:A161603 - cp's OEIS frontend

A161601 Positive integers k that are less than the value of the reversal of k's representation in binary.

11, 19, 23, 35, 37, 39, 43, 47, 55, 67, 69, 71, 75, 77, 79, 83, 87, 91, 95, 103, 111, 131, 133, 135, 137, 139, 141, 143, 147, 149, 151, 155, 157, 159, 163, 167, 171, 173, 175, 179, 183, 187, 191, 199, 203, 207, 215, 223, 239, 259, 261, 263, 265, 267, 269, 271

Offset: 1

Leroy Quet, Jun 14 2009

By "reversal" of k's representation in binary, it is meant: write k in binary, reverse the order of its digits, and read the result as a binary value.

This sequence contains only odd integers.

			37 = 100101_2; its digital reversal is 101001_2 = 41. Since 37 < 41, 37 is in this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A030101, A006995, A161602, A161603.

a := proc (n) local n2, sz, rv: n2 := convert(n, base, 2): sz := nops(n2): rv := add(n2[j]*2^(sz-j), j = 1 .. sz): if n < rv then n else end if end proc; seq(a(n), n = 1 .. 280); # Emeric Deutsch, Jun 28 2009

Select[Range[300],FromDigits[Reverse[IntegerDigits[#,2]],2]>#&] (* Harvey P. Dale, Mar 19 2016 *)

from itertools import count, islice
def A161601_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:nA161601_list = list(islice(A161601_gen(),20)) # Chai Wah Wu, Jan 19 2023

Extended by Emeric Deutsch, Jun 28 2009

Edited by Jon E. Schoenfield, Feb 24 2019

A161602 Positive integers k that are greater than the value of the reversal of k's binary representation.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 13, 14, 16, 18, 20, 22, 24, 25, 26, 28, 29, 30, 32, 34, 36, 38, 40, 41, 42, 44, 46, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 84, 86, 88, 89, 90, 92, 94, 96, 97, 98, 100, 101, 102, 104, 105, 106, 108, 109

Offset: 1

Leroy Quet, Jun 14 2009

By "reversal" of k's binary representation, it is meant: write k in binary, reverse the order of its digits, and read the result as a binary value.

This sequence contains all the positive even integers.

			29 in binary is 11101. Its digital reversal is 10111, which is 23 in decimal. Since 29 > 23, 29 is in this sequence.

Jonathan Frech, Table of n, a(n) for n = 1..10000

Cf. A030101, A006995, A161601, A161603 (odd terms).

Cf. A071590 (using decimal reversal).

Select[Range[109], # > IntegerReverse[#, 2] &] (* Michael De Vlieger, Apr 07 2021 *)

isok(k) = k > fromdigits(Vecrev(binary(k)), 2); \\ Michel Marcus, Apr 06 2021

from itertools import count, islice
def A161602_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:n>int(bin(n)[-1:1:-1],2),count(max(startvalue,1)))
A161602_list = list(islice(A161602_gen(),20)) # Chai Wah Wu, Jan 19 2023

More terms from Max Alekseyev, Sep 11 2009

cp's OEIS Frontend

A161601 Positive integers k that are less than the value of the reversal of k's representation in binary.

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