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A173418 Primes formed by the initial digits of the decimal expansion of 1/(Golden Ratio).

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%I A173418 #16 Jul 17 2025 08:20:10
%S A173418 61,61803398874989
%N A173418 Primes formed by the initial digits of the decimal expansion of 1/(Golden Ratio).
%C A173418 The next term consists of the first 887 digits of 1/(Golden Ratio) and is too large to show here.
%H A173418 Amiram Eldar, <a href="/A173418/b173418.txt">Table of n, a(n) for n = 1..3</a>
%H A173418 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Phi-Prime.html">Phi-Prime</a>.
%p A173418 Digits := 1000: n0 := evalf((sqrt(5)-1)/2): for i from 1 to 10000 do t1 := trunc(10^i*n0): if isprime(t1) then print(t1): fi: od:
%t A173418 With[{gr=RealDigits[1/GoldenRatio,10,1000][[1]]}, Select[Table[ FromDigits[ Take[ gr,n]], {n,1000}], PrimeQ]] (* _Harvey P. Dale_, Oct 17 2012 *)
%Y A173418 Cf. A065868, A094214.
%K A173418 nonn,base,bref
%O A173418 1,1
%A A173418 _Michel Lagneau_, Feb 17 2010