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 A349519 a(n)=x is the least prime with pi(x,4,3) - pi(x,4,1) = 1-n where pi(x,4,k) is the number of primes 4*j + k <= x. 1
 2, 26861, 616897, 616909, 616933, 623641, 623653, 623669, 623681, 12315529, 12315581, 12315613, 12315617, 12362653, 12362657, 12362717, 12362741, 12362981, 12362989, 12365033, 12365057, 12365153, 12365173, 12365201, 12366589, 951821281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The difference d(x) = pi(x,4,3) - pi(x,4,1) changes sign infinitely often, see link "Prime Quadratic Effect". But this does not say anything about the amplitudes of these oscillations. For diagrams, see A349518, "Oscillations of d(x)". If d(x) has no lower limit, the current sequence is infinite. Regarding the upper limit, see A349518. Note the gaps between 2, 26861 and 616897, 623681 and 12315529, 12366589 and 951821281. LINKS Eric Weisstein's World of Mathematics, Prime Quadratic Effect. EXAMPLE primes 4*j+1: 5, 13, 17, ... 4*j+3: 3, 7, 11, ... d(x) = pi(x,4,3) - pi(x,4,1) . n x pi(x,4,3) pi(x,4,1) d(x)=1-n? - ----- --------- --------- ----------- 1 2 0 0 0=0 true a(1) = 2 2 3 1 0 1=-1 false a(2) != 3 2 5 1 1 2=-1 false a(2) != 5 ........................... 2 26861 1472 1473 -1=-1 true a(3) = 26861 PROG (Maxima) block(w:[2], su:0, sum:0, n:1, p:2, nmax: 25, /* returns nmax terms */ while n

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)