A175392 - OEIS

%I #14 Nov 08 2018 21:11:11

%S 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,

%T 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,

%U 35,8,18,11,19,13,19,19,4,10,10,10,4,11,11,4,11,10,91

%N a(n) is the smallest positive integer that, when written in binary, occurs in binary A154809(n) but not in binary A030101(A154809(n)).

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

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

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

%C 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.

%H Rémy Sigrist, <a href="/A175392/b175392.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

%o 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

%Y Cf. A030101, A154809.

%K base,nonn

%O 1,1

%A _Leroy Quet_, Apr 28 2010

%E More terms from _Rémy Sigrist_, Nov 08 2018