A245470 Smallest multiple of n such that, when expressed in binary, in the string of bits the binary representation of n occurs after the n-1 most significant bits.

1, 6, 15, 36, 85, 150, 287, 1032, 2169, 4170, 8283, 16428, 32877, 65646, 131295, 524304, 1048849, 2097234, 4194611, 8388660, 16777845, 33554774, 67109239, 134217816, 268436025, 536871322, 1073742075, 2147483772, 4294967773, 8589935070, 17179869695, 68719476768, 137438955489, 274877908002, 549755814755, 1099511627940

Offset

1,2

Comments

For n>1, let d be the number of bits in n, and n' = n/gcd(n,2^d) = n/2^valuation(n,2) = A000265(n). Then a(n) = (2^{n-2}+mod(-(2^{n-2}),n')) * 2^d + n. (The mod function used here always returns a nonnegative result; e.g. mod(-2,7) = 5.) The alternative to use n/p^valuation(n,p) instead of gcd(n,p^d) works in any prime base p.

The word "after" in the definition can be interpreted as either "immediately after" or "at some point after" - the resulting sequence is the same.

Links

Table of n, a(n) for n=1..36.

Example

a(4) = 36 = 100100_2; 100, the binary representation of 4, occurs after 4-1 = 3 bits.

Prog

(PARI) numbit(n)=my(r=1); while(n>=2, n\=2; r++); r a(n) = my(k, m); if(n<=1, n, k=2^numbit(n); m=2^(n-2); (-m%(n\gcd(n, k))+m)*k+n) \\ Could use 2^valuation(n, 2) instead of gcd(n, k).

Crossrefs

Cf. A079847, A000265.

Sequence in context: A324221 A177206 A128443 * A135854 A221905 A083011

Adjacent sequences: A245467 A245468 A245469 * A245471 A245472 A245473

Keyword

nonn,base

Author

Franklin T. Adams-Watters, Jul 25 2014

Status

approved