A270968 Reduced 5x+1 function R applied to the odd integers: a(n) = R(2n-1), where R(k) = (5k+1)/2^r, with r as large as possible.

3, 1, 13, 9, 23, 7, 33, 19, 43, 3, 53, 29, 63, 17, 73, 39, 83, 11, 93, 49, 103, 27, 113, 59, 123, 1, 133, 69, 143, 37, 153, 79, 163, 21, 173, 89, 183, 47, 193, 99, 203, 13, 213, 109, 223, 57, 233, 119, 243, 31, 253, 129, 263, 67, 273, 139, 283, 9, 293, 149, 303

Offset: 1

Author

Michel Lagneau, Mar 27 2016

Keywords

• nonn
• easy

Comments

The odd-indexed terms a(2i+1) = 10i+3 = A017305(i), i>=0;

a(4i+4) = 10i+9 = A017377(i), i>=0;

a(8i+6) = 10i+7 = A017353(i), i>=0;

a(16i+2) = 10i+1 = A017281(i), i>=0.

Note that a(n) = a(16n-6) = a(6n-2)/3. No multiple of 5 is in this sequence.

a(n) = R(2n-1) < 2n-1 for n = 2, 6, 10, ..., 2+4i,...

Examples

			a(4)=9 because (2*4-1) = 7  -> (5*7+1)/2^2 = 9.
		

Crossrefs

Cf. A075677, A017281, A017305, A017353, A017377, A133423, A133424, A174795, A133419, A133420, A232711, A259207, A267969.

Programs

Mathematica

nextOddK[n_] := Module[{m=5n+1}, While[EvenQ[m], m=m/2]; m]; (* assumes odd n *) Table[nextOddK[n], {n, 1, 200, 2}]

PARI

a(n) = my(m = 2*n-1, c = 5*m+1); c/2^valuation(c, 2); \\ Michel Marcus, Mar 27 2016

Formula

a(n) = A000265(A017341(n-1)). - Michel Marcus, Mar 27 2016