The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A300005 Index of first occurrence of 2n in A300004 (or -1 of 2n does not occur), where A300004 are first differences of numbers not congruent to A000045(k) modulo A000045(k+1) for any k > 1. 1
 1, 0, 5, 26, 14, 100, 323, 1671, 4293, 10934, 208741, 753123, 627460, 87918559, 1137656208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS It is only conjectured that every even number occurs in sequence A300004. It would be interesting to know whether there are patterns or formulae for the indices at which the respective even numbers occur in. As can be seen from a(2) = 0, sequence A300004 has been chosen to be 0-indexed, as for A292794. LINKS FORMULA a(n) = min { k | 2n = A300004(k) = A292794(k+1) - A292794(k) }. EXAMPLE Index n| gap 2n |   a(n)   | A292794(a(n))   with a(n) = the smallest k    1   |    2   |     1    |       4         such that  A300004(k) = 2n    2   |    4   |     0    |       0         = A292794(k+1) - A292794(k)    3   |    6   |     5    |      16    4   |    8   |    26    |     106    5   |   10   |    14    |      54    6   |   12   |    100   |     444    7   |   14   |    323   |     1456    8   |   16   |   1671   |     7614    9   |   18   |   4293   |    19602   10   |   20   |   10934  |    49966   11   |   22   |  208741  |    954384   12   |   24   |  753123  |   3443356   13   |   26   |  627460  |   2868820   14   |   28   | 87918559 |  401976096   15   |   30   |1137656208| 5201526136 PROG (PARI) A300005=List(); b=c=L=0; ng=2; for(n=1, oo, is_A292794(n)||next; c++; bittest(b, g=-L+L=n)&&next; b+=2^g; listput(A300005, [g, c-1, n-g]); g>ng&&next; listsort(A300005); for(i=ng/2, #A300005, A300005[i][1]>ng&&break; printf("%d, ", A300005[i]); ng+=2)) CROSSREFS Cf. A300004, A292794, A000045. Sequence in context: A106295 A057688 A259207 * A048269 A073069 A042281 Adjacent sequences:  A300002 A300003 A300004 * A300006 A300007 A300008 KEYWORD nonn,more AUTHOR M. F. Hasler, Mar 05 2018 EXTENSIONS a(14)-a(15) from Jacques Tramu, Feb 26 2018 STATUS approved

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

Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)