A385093 Primes preceded and followed by gaps whose quotient (value greater or equal to 1) is greater than 2 and less than 3.
331, 953, 1381, 1861, 2161, 2357, 2371, 2423, 2879, 3229, 3271, 3407, 3491, 3607, 3643, 3691, 3889, 4057, 4073, 4139, 4201, 4507, 4567, 4751, 4831, 4903, 4987, 5059, 5153, 5297, 5309, 5683, 5897, 6029, 6053, 6067, 6173, 6229, 6529, 6599, 6653, 6857, 7079, 7151, 7159, 7193, 7283, 7417, 7717, 7867, 7963
Offset: 1
Keywords
Examples
331 is a term because Max(331-317,337-331)/Min(331-317,337-331) = 14/6 = 2.3333. 953 is a term because Max(953-947,967-953)/Min(953-947,967-953) = 14/6 = 2.3333. 1381 is a term because Max(1381-1373,1399-1381)/Min(1381-1373,1399-1381) = 18/8 = 2.25.
Programs
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Mathematica
Prime/@Select[Range[3,1000],2
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PARI
forprime(P=3, 8000, my(M=P-precprime(P-1), Q=nextprime(P+1)-P, AR=max(M,Q)/min(M,Q)); if(AR>2 && AR<3, print1(P,", ")));
Formula
Conjecture: Limit_{n->oo} n / PrimePi(a(n)) = 1/6.
Comments