A321226 Describe the binary representation of n in binary and convert back to decimal.

2, 3, 14, 5, 28, 59, 22, 7, 30, 115, 238, 117, 44, 91, 30, 9, 56, 123, 462, 229, 476, 955, 470, 119, 46, 179, 366, 181, 60, 123, 38, 11, 58, 227, 494, 245, 924, 1851, 918, 231, 478, 1907, 3822, 1909, 940, 1883, 478, 233, 88, 187, 718, 357, 732, 1467, 726, 183

Offset: 0

Author

Rémy Sigrist, Nov 10 2018

Keywords

• nonn
• base

Comments

This sequence is a binary variant of the "Look and Say" sequence A045918.

There is only one fixed point: a(7) = 7.

Examples

			For n = 67:
- the binary representation of 67 is "1000011",
- we see, in binary: "1" "1", "100" "0", "10" "1",
- hence the binary representation of a(67) is "111000101",
- and a(67) = 453 in decimal.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A020330, A045918, A049190.

Programs

PARI

a(n, b=2) = if (n==0, return (b)); my (d=digits(b*n, b), v=0, w=0); d[#d] = -1; for (i=1, #d-1, w++; if (d[i]!=d[i+1], v = b*(v*b^#digits(w, b) + w) + d[i]; w = 0)); v

Formula

a(2^n - 1) = 2*n + 1 for any n > 0.

a(4*n + 1) = 4*a(2*n) + 3 for any n > 0.

a(4*n + 2) = 4*a(2*n + 1) + 2 for any n >= 0.

a(A020330(2*n)) = A020330(a(2*n)) for any n > 0.

a(A049190(n)) = A049190(n+1) for any n > 0.