OFFSET
38,1
COMMENTS
The offset is 38, because up to that point the terms are not integers.
It appears that in A373390 the primes up to and including 157 (which is A373390(335)) appear irregularly. The next prime is 163 = A373390(350). So there is a possibility that ignoring the first 347 or so terms of A373390 may make it easier to analyze. A formula or other explanation for the present sequence would be of great help.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 38..6266
EXAMPLE
The first 38 terms of the first differences of A373792, halved, are
0, 5, -5, 29/2, -15, 23/2, -23/2, 27, -19/2, -35/2, 41, -41/2, 3, 3, 61/2, -49/2, -65/2, 71/2, 67/2, 4, 4, 9, 3, -77/2, 97/2, 3, 7, -2, 2, 16, 3, 8, 1, 12, 0, -137/2, 161/2, 4,
and that final 4 is the leading term of the present sequence.
MATHEMATICA
With[{s = Import["https://oeis.org/A373390/b373390.txt", "Data"][[All, -1]]}, 1/2*Differences@ MapIndexed[s[[#1 - 1]] - Prime@ First[#2] &, Values[KeySort@ KeySelect[PositionIndex[s], PrimeQ]][[All, 1]] ][[38 ;; -1]] ] (* Michael De Vlieger, Jun 29 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 29 2024
STATUS
approved