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A175392 a(n) is the smallest positive integer that, when written in binary, occurs in binary A154809(n) but not in binary A030101(A154809(n)). 1
2, 2, 2, 2, 10, 11, 2, 6, 2, 2, 18, 19, 4, 11, 11, 2, 6, 6, 2, 6, 2, 2, 34, 35, 18, 18, 19, 19, 4, 10, 42, 11, 4, 11, 11, 2, 6, 6, 4, 6, 22, 23, 2, 6, 6, 14, 2, 6, 2, 2, 66, 67, 34, 34, 35, 35, 8, 18, 11, 19, 13, 19, 19, 4, 10, 10, 10, 4, 11, 11, 4, 11, 10, 91 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A154809(n) is the n-th positive integer that is not a palindrome when written in binary.

A030101(n) is the decimal value of the digits of binary n written in backwards order.

No substring in binary n is absent from binary A030101(n) if n is a palindrome when written in binary.

It is immaterial if the leading 0's are included as part of A030101(A154809(n)) when checking if a particular substring is part of it, because the binary representations of all substrings begin with 1.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

EXAMPLE

20 in binary is 10100. A030101(20) = 5, which is 00101 = 101 in binary. The positive integers that occur as substrings of 10100 when written in binary are 1 (1 in binary), 2 (10 in binary), 4 (100 in binary), 5 (101 in binary), 10 (1010 in binary), and 20 (10100 in binary). The binary substring with the largest decimal value not present in (00)101 is 100, which is 4 in decimal. So a(20) = 4.

PROG

(PARI) in(abc, b) = my (m=2^#binary(b)); while (abc >= b, if (abc%m==b, return (1), abc\=2)); return (0)

for (v=1, 91, my (w=fromdigits(Vecrev(binary(v)), 2)); if (v!=w, for (k=1, oo, if (in(v, k) && !in(w, k), print1 (k ", "); break)))) \\ Rémy Sigrist, Nov 08 2018

CROSSREFS

Cf. A030101, A154809.

Sequence in context: A249768 A217503 A165466 * A289910 A112727 A164918

Adjacent sequences:  A175389 A175390 A175391 * A175393 A175394 A175395

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Apr 28 2010

EXTENSIONS

More terms from Rémy Sigrist, Nov 08 2018

STATUS

approved

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Last modified December 5 04:10 EST 2021. Contains 349530 sequences. (Running on oeis4.)