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

Author

Marc LeBrun, Oct 18 2001

Keywords

• base
• easy
• nonn
• tabl

Examples

			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.
		

Crossrefs

Cf. A065158, A065159, A065160.

Programs

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

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.