A119381 Primes p(n) for which (p(n-1) + p(n+2)) / p(n) = 2.
37, 67, 277, 479, 613, 631, 809, 1297, 1471, 1607, 1663, 1721, 1783, 1867, 1901, 1931, 1993, 2137, 2377, 2411, 2521, 2683, 2797, 2879, 3359, 3571, 3917, 4391, 4513, 4621, 5413, 5437, 5477, 5647, 6299, 7321, 7393, 7873, 7901, 8087, 8819, 9007, 10301
Offset: 1
Examples
In the ordered set of primes we have ...271,277,281,283... and (271+283)/277 = 2, therefore 277 belongs in this sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Prime[Select[Range[2, 1500], (Prime[ # - 1] + Prime[ # + 2])/(Prime[ # ]) == 2 &]] (* Stefan Steinerberger, Jul 26 2006 *) Select[Partition[Prime[Range[1300]],4,1],(#[[1]]+#[[4]])/#[[2]]==2&][[;;,2]] (* Harvey P. Dale, Aug 04 2024 *)
Formula
a(n) = Prime(A119382(n)), where Prime(n) is the n-th prime. - Stefan Steinerberger, Jul 26 2006
Extensions
More terms from Stefan Steinerberger, Jul 26 2006