A292410 Difference between (2n+1)^2 and highest power of 2 less than or equal to (2n+1)^2.

0, 1, 9, 17, 17, 57, 41, 97, 33, 105, 185, 17, 113, 217, 329, 449, 65, 201, 345, 497, 657, 825, 1001, 161, 353, 553, 761, 977, 1201, 1433, 1673, 1921, 129, 393, 665, 945, 1233, 1529, 1833, 2145, 2465, 2793, 3129, 3473, 3825, 89, 457, 833, 1217, 1609, 2009, 2417, 2833, 3257

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

a(n) = A053645(A016754(n)). - Michel Marcus, Sep 16 2017

Example

a(0) = 1^2 - 2^0 =  0.
a(1) = 3^2 - 2^3 =  1.
a(2) = 5^2 - 2^4 =  9.
a(3) = 7^2 - 2^5 = 17.
a(4) = 9^2 - 2^6 = 17.

Maple

seq((2*n+1)^2 - 2^ilog2((2*n+1)^2), n=0..100); @ Robert Israel, Oct 19 2017

Mathematica

Table[# - 2^Floor@ Log2@ # &[(2 n + 1)^2], {n, 0, 53}] (* Michael De Vlieger, Sep 18 2017 *)

Prog

(PARI) a(n) = my(k = 0); while(2^k < (2*n+1)^2, k++); if (k, k--); (2*n+1)^2 - 2^k; \\ Michel Marcus, Sep 16 2017

Crossrefs

Cf. A000079 (2^n), A016754 (odd squares), A053645 (distance to power of 2), A056577.

Sequence in context: A184938 A103707 A271641 * A004751 A134104 A124966

Adjacent sequences: A292407 A292408 A292409 * A292411 A292412 A292413

Keyword

nonn,look

Author

Zhandos Mambetaliyev, Sep 15 2017

Extensions

More terms from Michel Marcus, Sep 16 2017

Status

approved