A233671 Numbers k such that prime(k)^2 < prime(k-1)*prime(k+1).

2, 4, 6, 8, 9, 11, 14, 15, 18, 21, 23, 24, 27, 29, 30, 32, 34, 36, 39, 42, 44, 46, 50, 51, 53, 58, 61, 62, 65, 66, 68, 70, 71, 72, 76, 77, 79, 80, 82, 84, 86, 87, 90, 91, 94, 96, 97, 99, 101, 105, 106, 110, 114, 117, 118, 121, 123, 124, 125, 127, 132, 135

Offset: 1

Author

Clark Kimberling, Dec 14 2013

Keywords

• nonn
• easy

Comments

If 1 is appended to A046868, the resulting sequence is the complement of A233671. Does A233671 have asymptotic density 1/2? Does every positive integer occur infinitely many times in the difference sequence of A233671?

Examples

			a(1) = 2 because 3^2 < 2*5.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046868, A000040.

Programs

Mathematica

Select[Range[2, 200], Prime[#]^2 < Prime[# - 1]*Prime[# + 1] &]
PrimePi[#]&/@Select[Partition[Prime[Range[200]],3,1],#[[2]]^2<(#[[1]] #[[3]])&][[All,2]] (* Harvey P. Dale, Dec 09 2021 *)