The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A178414 Least odd number in the Collatz (3x+1) preimage of odd numbers not a multiple of 3. 3
 1, 3, 9, 7, 17, 11, 25, 15, 33, 19, 41, 23, 49, 27, 57, 31, 65, 35, 73, 39, 81, 43, 89, 47, 97, 51, 105, 55, 113, 59, 121, 63, 129, 67, 137, 71, 145, 75, 153, 79, 161, 83, 169, 87, 177, 91, 185, 95, 193, 99, 201, 103, 209, 107, 217, 111, 225, 115, 233, 119, 241, 123, 249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The odd non-multiples of 3 are 1, 5, 7, 11,... (A007310). The odd multiples of 3 have no odd numbers their Collatz pre-image. The next odd number in the Collatz iteration of a(2n) is 6n-1. The next odd number in the Collatz iteration of a(2n+1) is 6n+1. For each non-multiple of 3, there are an infinite number of odd numbers in its Collatz pre-image. For example: Odd pre-images of 1: 1, 5, 21, 85, 341,... (A002450) Odd pre-images of 5: 3, 13, 53, 213, 853,... (A072197) Odd pre-images of 7: 9, 37, 149, 597, 2389,... Odd pre-images of 11: 7, 29, 117, 469, 1877,...(A072261) In each case, the pre-image sequence is t(k+1) = 4*t(k) + 1 with t(0)=a(n). The array of pre-images is in A178415. a(n) = A047529(P(n)), with the permutation P(n) = A006368(n-1) + 1, for n >= 1. This shows that this sequence gives the numbers {1, 3, 7} (mod 8) uniquely. - Wolfdieter Lang, Sep 21 2021 LINKS Matthew House, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA a(n) = (n - 1)*(3 - (-1)^n) + 1. [Bogart B. Strauss, Sep 20 2013, adapted to the offset by Matthew House, Feb 14 2017] From Matthew House, Feb 14 2017: (Start) G.f.: x*(1 + 3*x + 7*x^2 + x^3)/((1 - x)^2*(1 + x)^2). a(n) = 2*a(n-2) - a(n-4). (End) From Philippe Deléham, Nov 06 2023: (Start) a(2*n) = 4*n-1, a(2*n+1) = 8*n+1. a(n) = 2*A022998(n-1)+1. a(n) = 2*A114752(n)-1. (End) MATHEMATICA Riffle[1+8*Range[0, 50], 3+4*Range[0, 50]] CROSSREFS Cf. A002450, A006368, A007310, A022998, A047529, A072197, A072261, A114752. Sequence in context: A146179 A294734 A214661 * A220654 A302158 A337974 Adjacent sequences: A178411 A178412 A178413 * A178415 A178416 A178417 KEYWORD nonn,easy AUTHOR T. D. Noe, May 28 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 16 11:02 EDT 2024. Contains 373429 sequences. (Running on oeis4.)