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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
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
Sequence in context: A089174 A321700 A020636 * A265760 A071200 A038921
KEYWORD
nonn
AUTHOR
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.)