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%I #16 Mar 20 2018 11:34:45
%S 1,0,5,26,14,100,323,1671,4293,10934,208741,753123,627460,87918559,
%T 1137656208
%N 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.
%C It is only conjectured that every even number occurs in sequence A300004.
%C It would be interesting to know whether there are patterns or formulae for the indices at which the respective even numbers occur in.
%C As can be seen from a(2) = 0, sequence A300004 has been chosen to be 0-indexed, as for A292794.
%F a(n) = min { k | 2n = A300004(k) = A292794(k+1) - A292794(k) }.
%e Index n| gap 2n | a(n) | A292794(a(n)) with a(n) = the smallest k
%e 1 | 2 | 1 | 4 such that A300004(k) = 2n
%e 2 | 4 | 0 | 0 = A292794(k+1) - A292794(k)
%e 3 | 6 | 5 | 16
%e 4 | 8 | 26 | 106
%e 5 | 10 | 14 | 54
%e 6 | 12 | 100 | 444
%e 7 | 14 | 323 | 1456
%e 8 | 16 | 1671 | 7614
%e 9 | 18 | 4293 | 19602
%e 10 | 20 | 10934 | 49966
%e 11 | 22 | 208741 | 954384
%e 12 | 24 | 753123 | 3443356
%e 13 | 26 | 627460 | 2868820
%e 14 | 28 | 87918559 | 401976096
%e 15 | 30 |1137656208| 5201526136
%o (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))
%Y Cf. A300004, A292794, A000045.
%K nonn,more
%O 1,3
%A _M. F. Hasler_, Mar 05 2018
%E a(14)-a(15) from _Jacques Tramu_, Feb 26 2018