A385109 If n is 5 (mod 8) then apply n = (n-1)/4 until the result is not equivalent 5 (mod 8); otherwise a(n) = n.

0, 1, 2, 3, 4, 1, 6, 7, 8, 9, 10, 11, 12, 3, 14, 15, 16, 17, 18, 19, 20, 1, 22, 23, 24, 25, 26, 27, 28, 7, 30, 31, 32, 33, 34, 35, 36, 9, 38, 39, 40, 41, 42, 43, 44, 11, 46, 47, 48, 49, 50, 51, 52, 3, 54, 55, 56, 57, 58, 59, 60, 15, 62, 63, 64, 65, 66, 67, 68, 17, 70, 71, 72, 73, 74, 75, 76, 19

Offset

0,3

Comments

a(8*n + 5) = A347840(n).

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Formula

Recurrence: a(1) = 1, a(2n) = 2n, a(4n+3) = 4n+3, a(8n+1) = 8n+1, a(8n+5) = a(2n+1).

Example

a(37): n is 5 (mod 8), so n = (37-1)/4 = 9, which is 1 (mod 8), so a(37) = 9.
a(53): n is 5 (mod 8), so n = (53-1)/4 = 13, which is 5 (mod 8), so n = (13-1)/4 = 3, and, as 3 is 3 (mod 8), a(53) = 3.

Mathematica

A385109[n_] := NestWhile[(# - 1)/4 &, n , Mod[#, 8] == 5 &];
Array[A385109, 100, 0] (* Paolo Xausa, Jun 25 2025 *)

Prog

(PARI) a(n) = if(n%8!=5, n, m=n; while(m%8==5, m=(m-1)/4); m)

Crossrefs

Cf. A347840.

Sequence in context: A132739 A060791 A235380 * A116912 A377938 A255690

Adjacent sequences: A385106 A385107 A385108 * A385110 A385111 A385112

Keyword

nonn

Author

Ralf Stephan, Jun 18 2025

Status

approved