A348762 a(n) = A000265((n-8)*(n+8)).

17, 9, 57, 5, 105, 33, 161, 3, 225, 65, 297, 21, 377, 105, 465, 1, 561, 153, 665, 45, 777, 209, 897, 15, 1025, 273, 1161, 77, 1305, 345, 1457, 3, 1617, 425, 1785, 117, 1961, 513, 2145, 35, 2337, 609, 2537, 165, 2745, 713, 2961, 3, 3185, 825, 3417, 221, 3657

Offset

9,1

Comments

Shares 495 initial terms with A061049. First difference is A061049(504)=62 vs. a(504)=31.

Links

Table of n, a(n) for n=9..61.

Formula

a(n) = A000265(A098849(n-8)).

Example

a( 9) = A000265(( 9-8)*( 9+8)) = A000265( 17) = 17,
a(10) = A000265((10-8)*(10+8)) = A000265( 36) = 9,
a(11) = A000265((11-8)*(11+8)) = A000265( 57) = 57,
a(12) = A000265((12-8)*(12+8)) = A000265( 80) = 5,
a(13) = A000265((13-8)*(13+8)) = A000265(105) = 105.

Mathematica

a[n_] := (n - 8)*(n + 8)/2^IntegerExponent[(n - 8)*(n + 8), 2]; Array[a, 53, 9] (* Amiram Eldar, Nov 22 2021 *)

Prog

(Ruby) p (9..27).map { |n| x = (n-8)*(n+8); x /= 2 while x.even?; x }
(PARI) A000265(n) = n >> valuation(n, 2);
a(n) = A000265((n-8)*(n+8));
[a(n)|n<-[9..27]]
(Python)
def A348762(n):
    a, b = divmod(n*n-64, 2)
    while b == 0:
        a, b = divmod(a, 2)
    return 2*a+b # Chai Wah Wu, Dec 05 2021

Crossrefs

Cf. A061049, A069834, A000265, A098849.

Sequence in context: A083308 A113779 A061049 * A166524 A106791 A040274

Adjacent sequences: A348759 A348760 A348761 * A348763 A348764 A348765

Keyword

nonn

Author

Simon Strandgaard, Oct 31 2021

Status

approved