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

0,1

Comments

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

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

Links

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

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.

Example

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.

Prog

(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

Crossrefs

Cf. A020330, A045918, A049190.

Sequence in context: A249826 A352407 A364037 * A337329 A329365 A119616

Adjacent sequences: A321223 A321224 A321225 * A321227 A321228 A321229

Keyword

nonn,base

Author

Rémy Sigrist, Nov 10 2018

Status

approved