A186205 The first n-digit prime in the decimal expansion of the golden ratio.

3, 61, 887, 9887, 39887, 339887, 1618033, 65638117, 398874989, 1772030917, 38622235369, 803398874989, 1618033988749, 61803398874989, 586834365638117, 8343656381177203, 69317931800607667, 484754088075386891

Offset

1,1

Comments

The Golden ratio is (1+sqrt(5))/2 = 1.618033988749894848204586834....

Links

Table of n, a(n) for n=1..18.

Maple

Digits := 10000: p0 := evalf((1+sqrt(5))/2):for d from 1 to 20 do: id:=0:for
  i from 0 to 50000 while(id=0) do :q0:=trunc(p0*10^(i+d-1)): x:= irem(q0, 10^d):
  if type(x, prime)=true and length(x)=d then printf(`%d, `, x):id:=1: else fi:od:od:

Mathematica

With[{c=RealDigits[GoldenRatio, 10, 100000][[1]]}, FromDigits/@Table[ SelectFirst[ Partition[c, n, 1], PrimeQ[FromDigits[#]] && IntegerLength[ FromDigits[#]]==n&], {n, 18}]] (* Harvey P. Dale, Aug 21 2017 *)

Crossrefs

Cf. A001622.

Sequence in context: A102720 A120308 A279381 * A224451 A239792 A009476

Adjacent sequences: A186202 A186203 A186204 * A186206 A186207 A186208

Keyword

nonn,base

Author

Michel Lagneau, Feb 15 2011

Status

approved