A065157 Table of binary string substitutions: a(i,j) is obtained by substituting i for each 1-bit in j.

1, 2, 2, 3, 4, 3, 4, 6, 10, 4, 5, 8, 15, 8, 5, 6, 10, 36, 12, 18, 6, 7, 12, 45, 16, 27, 20, 7, 8, 14, 54, 20, 68, 30, 42, 8, 9, 16, 63, 24, 85, 72, 63, 16, 9, 10, 18, 136, 28, 102, 90, 292, 24, 34, 10, 11, 20, 153, 32, 119, 108, 365, 32, 51, 36, 11, 12, 22, 170, 36, 264, 126, 438, 40, 132, 54, 74, 12

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Formula

Table origin is a(1,1).

a(1,n) = a(n,1) = n.

a(0,n) = a(n,0) = 0.

a(i,j) = A065158(i,j)*i.

a(n,n) = A065159(n) = A065160(n)*n.

Example

a(3,5): 5 = 101_2 -> (3)0(3) = (11)0(11)_2 = 11011_2 = 27.
a(5,3): 3 = 11_2 -> (5)(5) = (101)(101)_2 = 101101_2 = 45.

Prog

(PARI) T(n, k) = my(bk=binary(k), sn=Str(fromdigits(binary(n))), s=""); for (i=1, #bk, if (bk[i] == 1, s=concat(s, sn), s=concat(s, "0"))); fromdigits(apply(eval, Vec(s)), 2); \\ Michel Marcus, Feb 11 2023

Crossrefs

Cf. A065158, A065159, A065160.

Sequence in context: A131923 A119457 A241356 * A235804 A051597 A084193

Adjacent sequences: A065154 A065155 A065156 * A065158 A065159 A065160

Keyword

base,easy,nonn,tabl

Author

Marc LeBrun, Oct 18 2001

Status

approved