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 A141657 a(n) = (prime(2*m)-prime(m))/6 where m is the n-th positive integer such that (prime(2*m)-prime(m))/6 is prime. 1
 2, 3, 7, 11, 13, 17, 19, 23, 71, 71, 83, 83, 89, 101, 103, 127, 163, 167, 191, 193, 199, 239, 239, 251, 263, 277, 307, 307, 307, 317, 331, 337, 389, 443, 463, 487, 509, 509, 557, 659, 691, 787, 797, 863, 881, 883, 887, 887, 953, 971, 977, 991, 1019, 1063, 1069 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 EXAMPLE For m=4, (p(2*4) - p(4))/6 = (19 - 7)/6 = 2 = a(1). For m=5, (p(2*5) - p(5))/6 = (29 - 11)/6 = 3 = a(2). For m=10, (p(2*10) - p(10))/6 = (71 - 29)/6 = 7 = a(3). For m=15, (p(2*15) - p(15))/6 = (113 - 47)/6 = 11 = a(4). For m=16, (p(2*16) - p(16))/6 = (131 - 53)/6 = 13 = a(5), etc. MATHEMATICA Select[Table[(Prime[2n]-Prime[n])/6, {n, 1000}], PrimeQ[#]&] (* Harvey P. Dale, Jun 18 2023 *) CROSSREFS Cf. A000040, A072473. Sequence in context: A089174 A321700 A020636 * A265760 A071200 A038921 Adjacent sequences: A141654 A141655 A141656 * A141658 A141659 A141660 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Sep 18 2008 EXTENSIONS 19, 23 inserted, one instance of 331 removed, 577 removed and extended by R. J. Mathar, Oct 04 2008 Definition clarified by Harvey P. Dale, Jun 18 2023 Definition clarified by David A. Corneth, Jun 18 2023 STATUS approved

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Last modified February 22 18:56 EST 2024. Contains 370260 sequences. (Running on oeis4.)