A276198 Smallest prime >= decimal expansion of phi truncated to n places (A011551), where phi is the golden ratio (A001622).

2, 17, 163, 1619, 16183, 161807, 1618033, 16180349, 161803403, 1618033999, 16180339933, 161803398917, 1618033988749, 16180339887557, 161803398874991, 1618033988749901, 16180339887498961, 161803398874989661, 1618033988749894853, 16180339887498948503, 161803398874989484891

Offset: 0

Author

Ilya Gutkovskiy, Aug 24 2016

Keywords

• nonn
• base

Examples

			a(5) = 161807, since this is the smallest prime >= floor(phi*10^5) = 161803.
phi = 1.61803398874989484820458683436563811772...
		

Links

• Eric Weisstein's World of Mathematics, Next Prime
• Eric Weisstein's World of Mathematics, Golden Ratio
• Eric Weisstein's World of Mathematics, Phi-Prime
• Index entries related to "constant primes"

Crossrefs

Cf. A000040, A000720, A001622, A007918, A011551, A064117, A064119.

Programs

Mathematica

Table[NextPrime[Floor[GoldenRatio 10^n] - 1], {n, 0, 20}]

Formula

a(n) = A007918(A011551(n)).

a(n) = A000040(A000720(A011551(n)-1)+1).

a(A064119(n)-1) = A064117(n).