cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A128050 Position of start of first occurrence of prime(n) after the decimal point in expansion of golden ratio phi.

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%I A128050 #15 Aug 01 2024 09:15:36
%S A128050 19,5,22,10,34,55,35,188,131,174,137,98,90,27,102,111,166,1,150,217,
%T A128050 479,44,25,13,81,458,1242,744,563,96,1602,186,97,995,259,939,1999,
%U A128050 1204,641,1191,43,833,1682,2833,2708,188,647,130,62,734,2337,1106,307,1156,2532
%N A128050 Position of start of first occurrence of prime(n) after the decimal point in expansion of golden ratio phi.
%H A128050 Paolo Xausa, <a href="/A128050/b128050.txt">Table of n, a(n) for n = 1..10000</a>
%e A128050 Golden ratio phi = 1.6180339887498948482045868343656381177... (see A001622).
%e A128050 First occurrence of prime(1) = 2 is at the 19th digit after the decimal point, hence a(1) = 19.
%e A128050 First occurrence of prime(5) = 11 starts at the 34th digit after the decimal point, hence a(5) = 34.
%t A128050 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 A128050 (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 A128050 Cf. A001622, A037024, A014777.
%K A128050 base,nonn
%O A128050 1,1
%A A128050 _Gregory Allen_, Feb 13 2007
%E A128050 Edited, corrected and extended by _Klaus Brockhaus_, Feb 15 2007