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%I #4 Mar 23 2021 21:32:33
%S 1,4,7,9,10,15,16,22,23,24,25,34,36,37,39,40,47,55,56,57,58,64,67,82,
%T 84,86,87,88,91,93,94,95,96,97,98,99,100,102,104,105,106,107,130,133,
%U 134,135,136,137,138,139,140,141,142,144,146,147,148,149,150,153
%N Numbers k such that there are more primes in the interval [4*k+1, 5*k] than there are in the interval [3*k+1, 4*k].
%C After a(876) = 11895, there are no more terms < 100000.
%C Conjecture: a(876) = 11895 is the final term.
%C There exist eight terms k for which A342068(k) != 5: A342068(k) = 2 for k = 1; A342068(k) = 3 for k = 47, 67, 95, and 1323; and A342068(k)=4 for k = 22, 57, and 102.
%e The intervals [1, 100], [101, 200], [201, 300], [301, 400], and [401, 500] contain 25, 21, 16, 16, and 17 primes, respectively (cf. A038822); 17 > 16, so 100 is a term of the sequence.
%Y Cf. A342068, A342069, A342070, A342071.
%K nonn
%O 1,2
%A _Jon E. Schoenfield_, Mar 23 2021
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