The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A342242

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A342242

For any n > 0, a(n) is the least positive number whose binary expansion is both a prefix and a suffix of the binary expansion of n; a(0) = 0.
(history; published version)

#11 by N. J. A. Sloane at Sun Mar 07 17:46:42 EST 2021

STATUS

proposed

approved

#10 by Rémy Sigrist at Sun Mar 07 15:22:25 EST 2021

STATUS

editing

proposed

#9 by Rémy Sigrist at Sun Mar 07 15:03:57 EST 2021

LINKS

Rémy Sigrist, <a href="/A342242/b342242.txt">Table of n, a(n) for n = 0..8192</a>

STATUS

approved

editing

Discussion

Sun Mar 07

15:22

Rémy Sigrist: added b-file

#8 by N. J. A. Sloane at Sun Mar 07 14:42:07 EST 2021

STATUS

proposed

approved

#7 by Rémy Sigrist at Sun Mar 07 14:14:55 EST 2021

STATUS

editing

proposed

#6 by Michael S. Branicky at Sun Mar 07 11:33:04 EST 2021

PROG

(Python)

def a(n):

b = bin(n)[2:]

for i in range(1, len(b)+1):

if b[:i] == b[-i:]: return int(b[:i], 2)

print([a(n) for n in range(80)]) # Michael S. Branicky, Mar 07 2021

#5 by Rémy Sigrist at Sun Mar 07 11:01:18 EST 2021

EXAMPLE

For n = 814:

- the binary expansion of 814 is "1100101110",

- "1" does not match "0",

- "11" does not match "10",

- "110" matches "110",

- so the binary representation of a(814) is "110",

- and a(814) = 6.

#4 by Rémy Sigrist at Sun Mar 07 08:10:24 EST 2021

COMMENTS

All terms belong to A091065.

FORMULA

a(a(n)) = a(n).

#3 by Rémy Sigrist at Sun Mar 07 08:08:27 EST 2021

FORMULA

a(n) <= n with equality iff n belongs to A091065.

a(n) = n mod 2^A342241(n).

CROSSREFS

Cf. A091065, A342241, A342241.

#2 by Rémy Sigrist at Sun Mar 07 06:21:24 EST 2021

NAME

allocated for Rémy Sigrist

For any n > 0, a(n) is the least positive number whose binary expansion is both a prefix and a suffix of the binary expansion of n; a(0) = 0.

DATA

0, 1, 2, 1, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 14, 1, 16, 1, 2, 1, 20, 1, 2, 1, 24, 1, 26, 1, 28, 1, 30, 1, 32, 1, 2, 1, 4, 1, 2, 1, 40, 1, 2, 1, 44, 1, 2, 1, 48, 1, 50, 1, 52, 1, 6, 1, 56, 1, 58, 1, 60, 1, 62, 1, 64, 1, 2, 1, 4, 1, 2, 1, 72, 1, 2, 1, 4, 1, 2, 1

OFFSET

0,3

LINKS

<a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

FORMULA

a(n) = 1 iff n is an odd number.

PROG

(PARI) a(n) = { my (b=if (n, binary(n), [0])); for (w=1, oo, if (b[1..w]==b[#b+1-w..#b], return (fromdigits(b[1..w], 2)))) }

CROSSREFS

Cf. A342241.

KEYWORD

allocated

nonn,base,easy

AUTHOR

Rémy Sigrist, Mar 07 2021

STATUS

approved

editing