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%I #15 Aug 01 2024 09:15:36
%S 19,5,22,10,34,55,35,188,131,174,137,98,90,27,102,111,166,1,150,217,
%T 479,44,25,13,81,458,1242,744,563,96,1602,186,97,995,259,939,1999,
%U 1204,641,1191,43,833,1682,2833,2708,188,647,130,62,734,2337,1106,307,1156,2532
%N Position of start of first occurrence of prime(n) after the decimal point in expansion of golden ratio phi.
%H Paolo Xausa, <a href="/A128050/b128050.txt">Table of n, a(n) for n = 1..10000</a>
%e Golden ratio phi = 1.6180339887498948482045868343656381177... (see A001622).
%e First occurrence of prime(1) = 2 is at the 19th digit after the decimal point, hence a(1) = 19.
%e First occurrence of prime(5) = 11 starts at the 34th digit after the decimal point, hence a(5) = 34.
%t Module[{p = Rest[First[RealDigits[GoldenRatio, 10, 10^4]]], n = 0, a}, Reap[While[(a = SequencePosition[p, IntegerDigits[Prime[++n]], 1]) != {}, Sow[a[[1, 1]]]]][[2, 1]]] (* _Paolo Xausa_, Aug 01 2024 *)
%o (Magma) k:=3000; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-1 + (Sqrt(elt<R | 5, 0>)+1) / elt<R | 2, 0>))), IntegerToString(NthPrime(n))) : n in [1..55] ]; /* _Klaus Brockhaus_, Feb 15 2007 */
%Y Cf. A001622, A037024, A014777.
%K base,nonn,changed
%O 1,1
%A _Gregory Allen_, Feb 13 2007
%E Edited, corrected and extended by _Klaus Brockhaus_, Feb 15 2007
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