A085200 -id:A085200 - cp's OEIS frontend

A085201 Array A(x,y): Position of the concatenation of binary strings A014486(x) & A014486(y) in A014486, listed antidiagonalwise as A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ...

0, 1, 1, 2, 2, 2, 3, 4, 4, 3, 4, 6, 9, 5, 4, 5, 9, 14, 10, 9, 5, 6, 11, 23, 15, 23, 10, 6, 7, 14, 28, 24, 37, 24, 11, 7, 8, 16, 37, 29, 65, 38, 25, 12, 8, 9, 19, 42, 38, 79, 66, 39, 26, 13, 9, 10, 23, 51, 43, 107, 80, 67, 40, 27, 23, 10, 11, 25, 65, 52, 121, 108, 81, 68, 41, 65, 24, 11

Offset: 0

Antti Karttunen, Jun 23 2003

This table is induced by the 2-ary form of the list-function 'append' present in the programming languages like Lisp, Scheme and Prolog.

Index entries for the sequences induced by list functions of Lisp

Transpose: A085202. Variant: A085203. Row 1: A085223, Column 1: A072795.

Cf. also A014486, A080300, A025581, A002262.

a(0, y)=y, a(x, y) = A072764bi(A072771(x), a(A072772(x), y))

a(x, y) = A080300(A085207bi(A014486(x), A014486(y))) = A085200(A085215bi(A071155(y), A071155(x)))

A085203 Array A(x,y): Position of the totally balanced binary string obtained by concatenating the binary strings A014486(x) & A014486(y) in such a way that the latter is inserted after the least significant 1-bit of the former, followed by the remaining 0-bits, if any. Listed antidiagonalwise as A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ...

Original entry on oeis.org

0, 1, 1, 2, 3, 2, 3, 5, 7, 3, 4, 8, 12, 8, 4, 5, 10, 21, 13, 17, 5, 6, 13, 26, 22, 31, 18, 6, 7, 15, 35, 27, 58, 32, 20, 7, 8, 18, 40, 36, 73, 59, 34, 21, 8, 9, 22, 49, 41, 100, 74, 62, 35, 22, 9, 10, 24, 63, 50, 115, 101, 76, 63, 36, 45, 10, 11, 27, 68, 64, 142, 116, 104, 77, 64, 87, 46

Offset: 0

Antti Karttunen, Jun 23 2003

This table is induced by the list-function 'app-to-xrt' whose Scheme-definition is given below, in the same way as A085201 is induced by the ordinary 'append'-function.

Transpose: A085204. Variant: A085201. Row 1: A085225, Column 1: A057548.

Cf. also A014486, A080300, A025581, A002262.

a(0, y) = y, a(x, y) = A057548(a(A072771(x), y)) if A072772(x)=0, otherwise A072764bi(A072771(x), a(A072772(x), y)).

a(x, y) = A080300(A085211bi(A014486(x), A014486(y))) = A085200(A085219bi(A071155(y), A071155(x))).

A085199 Inverse function of N -> N injection A071156.

Original entry on oeis.org

0, 1, 0, 2, 0, 3, 0, 0, 0, 4, 0, 5, 0, 0, 0, 6, 0, 7, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 10, 0, 0, 0, 11, 0, 12, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 15, 0, 0, 0, 16, 0, 17, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 0, 20, 0, 0, 0, 0, 0, 21, 0, 0, 0

Offset: 0

Antti Karttunen, Jun 14 2003

nonn

a(0)=0 because A071156(0)=0, but a(n) = 0 also for those n which do not occur as values of A071156. All positive natural numbers occur here once.

a(A071156(n)) = n for all n.

a(n) = A057164(A085200(n)).

cp's OEIS Frontend

A085201 Array A(x,y): Position of the concatenation of binary strings A014486(x) & A014486(y) in A014486, listed antidiagonalwise as A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ...

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A085199 Inverse function of N -> N injection A071156.

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