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A173428 The smallest prime appearing in the truncated version of the decimal expansion of (Golden Ratio)^n shifted iteratively left. 0

%I

%S 1618033,2618033988749,42360679,6854101,1109,179,2903,469787,

%T 760131556174964248389559523684316960024905121133959373,1229,

%U 19900502499874064149,32199689437,5210019193,8429

%N The smallest prime appearing in the truncated version of the decimal expansion of (Golden Ratio)^n shifted iteratively left.

%C The n-th power of the golden ratio A001622 is successively shifted left, building floor(A001622^n *10^k) for k = 0, 1, 2, 3,...

%C As soon as this becomes a prime, we let a(n) be this prime.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Phi-Prime.html">Phi-Prime</a>

%e 1618033 is the first prime found in the decimal expansion of Golden Ratio A001622, after 6 shifts to the left.

%e 2618033988749 is the first prime found in the decimal expansion of (Golden Ratio)^2, A104457.

%e 42360679 is the first prime found in the decimal expansion of (Golden Ratio)^3, A098317.

%p Digits := 200:for n from 1 to 50 do: n0 := evalf(((sqrt(5)+1)/2)^n): for p from 1 to 100 while (type(trunc(10^p*n0),prime)= false) do:od: n2:= trunc(10^p*n0): print (n2): od:

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Feb 18 2010

%E Edited by _R. J. Mathar_, Feb 24 2010

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Last modified August 15 13:20 EDT 2020. Contains 336504 sequences. (Running on oeis4.)