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It seems that the n-th prime p appears in A098550 at around position 2*p; if in fact A098550(w) = p then set a(n) =w-2*p.
1

%I #12 Mar 15 2022 13:33:29

%S -2,-3,-1,1,0,-3,-4,5,5,3,0,5,5,2,7,8,9,10,8,11,12,9,9,16,10,13,16,19,

%T 20,21,20,21,22,23,26,27,24,29,30,29,28,31,32,37,36,37,30,33,36,39,40,

%U 45,46,39,36,45,44,47,48,49,54,51,54,53,56,57,58,55,60,61,60,61,60,63,62,65,70,67,66,67,66,67,74

%N It seems that the n-th prime p appears in A098550 at around position 2*p; if in fact A098550(w) = p then set a(n) =w-2*p.

%C This is the amount by which p lags behind its expected position.

%H Rémy Sigrist, <a href="/A352195/b352195.txt">Table of n, a(n) for n = 1..10000</a> (first 633 terms from N. J. A. Sloane)

%H Rémy Sigrist, <a href="/A352195/a352195.gp.txt">PARI program</a>

%o (PARI) See Links section.

%Y Cf. A098550.

%K sign

%O 1,1

%A _N. J. A. Sloane_, Mar 14 2022