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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
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.
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
KEYWORD
nonn,more
AUTHOR
M. F. Hasler, Mar 05 2018
EXTENSIONS
a(14)-a(15) from Jacques Tramu, Feb 26 2018
STATUS
approved