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%I #22 Aug 06 2017 23:03:52
%S 3,10,53,191,478,538,1082,1277,1346,2498,3299,5147,12889,20849,28277,
%T 31454,338098,520526,546461,1050706,1761289,1965077,3467038,6085103,
%U 27348949,27915898,111108917,113652593,230126531,231902434,327764249,438981203,581755523,1837981759,2489382911
%N Upper ends of record gaps between numbers that are either prime or twice a prime.
%C The gap between 31397 and 31454 is due to the record prime gap between 31397 and 31469 being almost exactly twice the record prime gap between 15683 and 15727.
%H Giovanni Resta, <a href="/A290489/b290489.txt">Table of n, a(n) for n = 1..40</a>
%F a(n) = A290488(n) + A290541(n).
%e a(3) = 53 because the next number that is a prime or twice a prime after 47 is 53, and that is a record gap of size 6.
%t p = op = 2; r = 0; Reap[While[p < 10^6, p++; If[PrimeQ[p] || PrimeQ[p/2], g = p - op; If[g > r, Sow@p; r = g]; op = p]]][[2, 1]] (* _Giovanni Resta_, Aug 04 2017 *)
%Y Cf. A001751, A290488, A290541.
%K nonn
%O 1,1
%A _Bobby Jacobs_, Aug 03 2017
%E a(17)-a(35) from _Giovanni Resta_, Aug 04 2017
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