A104493 Numbers n for which the cube excess of the n-th prime is prime.

2, 5, 6, 8, 10, 19, 20, 23, 26, 28, 31, 48, 49, 50, 51, 52, 55, 56, 57, 59, 61, 65, 66, 99, 100, 105, 110, 112, 114, 117, 121, 125, 127, 170, 171, 173, 178, 184, 185, 186, 190, 192, 194, 196, 200, 201, 206, 208, 214, 270, 271, 272, 274, 277, 278, 279, 280, 282

Offset: 1

Author

Jonathan Vos Post, Mar 19 2005

Keywords

• easy
• nonn

Examples

			99 is an element of this sequence because the 99th prime is 523, 523 - 8^3 = 523-512 = 11 and 11 is prime. 100 is in this sequence because the 100th prime is 541 and 541-8^3 = 29, which is prime.
		

Crossrefs

Cf. A000040, A053186, A055400, A056892, A102821, A104492.

Programs

Mathematica

f[n_] := Block[{k = 1, p = Prime[n]}, While[k^3 < p, k++ ]; p - (k - 1)^3]; Select[ Range[ 284], PrimeQ[ f[ # ]] &] (* Robert G. Wilson v, Mar 19 2005 *)

Formula

n such that A055400(A000040(n)) is an element of A000040. n such that A104492(n) is prime.

Extensions

More terms from Robert G. Wilson v, Mar 19 2005