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)).

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

Offset: 1

Author

Leroy Quet, Apr 28 2010

Keywords

• base
• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A030101, A154809.

Programs

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

Extensions

More terms from Rémy Sigrist, Nov 08 2018