A037024 -id:A037024 - cp's OEIS frontend

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

19, 5, 22, 10, 34, 55, 35, 188, 131, 174, 137, 98, 90, 27, 102, 111, 166, 1, 150, 217, 479, 44, 25, 13, 81, 458, 1242, 744, 563, 96, 1602, 186, 97, 995, 259, 939, 1999, 1204, 641, 1191, 43, 833, 1682, 2833, 2708, 188, 647, 130, 62, 734, 2337, 1106, 307, 1156, 2532

Offset: 1

Gregory Allen, Feb 13 2007

			Golden ratio phi = 1.6180339887498948482045868343656381177... (see A001622).
First occurrence of prime(1) = 2 is at the 19th digit after the decimal point, hence a(1) = 19.
First occurrence of prime(5) = 11 starts at the 34th digit after the decimal point, hence a(5) = 34.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A001622, A037024, A014777.

k:=3000; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-1 + (Sqrt(elt)+1) / elt))), IntegerToString(NthPrime(n))) : n in [1..55] ]; /* Klaus Brockhaus, Feb 15 2007 */

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 *)

Edited, corrected and extended by Klaus Brockhaus, Feb 15 2007

A309343 Position of start of first occurrence of palindromic prime(n) after the decimal point in expansion of Pi.

Original entry on oeis.org

6, 9, 4, 13, 94, 852, 1096, 393, 728, 1944, 858, 934, 5229, 25, 405, 631, 647, 1259, 416, 1853, 78246, 182558, 13736, 53100, 38835, 58726, 54516, 97930, 8827, 11000, 69516, 5795, 183115, 161674, 320336, 41934, 55891, 71399, 65195, 189109, 21045, 49012

Offset: 1

Hauke Löffler, Jul 24 2019

			First occurrence of palindromic prime(5) = 11 starts at the 94th digit after the decimal point, hence a(5) = 94.

Cf. A002385, A037024, A000796, A014777.

def postionInPi(n):
  return str(N(pi, 2000000))[1:].find(str(n))
[ postionInPi(i) for i in A002385[0:200] ]

A341442 a(n) is the position of the start of the first occurrence of prime(n) after the decimal point in the expansion of e.

Original entry on oeis.org

4, 17, 11, 1, 200, 27, 88, 108, 16, 131, 189, 270, 124, 134, 25, 18, 11, 242, 59, 1, 157, 168, 205, 221, 35, 195, 941, 283, 1748, 355, 370, 4604, 1574, 1998, 223, 413, 201, 483, 232, 599, 2875, 120, 1382, 108, 607, 1067, 426, 2494, 1329, 517, 178, 574, 2133

Offset: 1

Gregory Allen, Feb 11 2021

			The first position at which prime(1)=2 occurs to the right of the decimal point in e=2.71828... is the 4th digit after the decimal point, so a(1)=4.

Cf. A000040, A001113, A037024, A078197, A128050.

en=Characters[ToString@N[E,10000]];
For[x=1,x<=100,x++,Print["x=",x," ",prn=Prime[x]," ",pos=First[SequencePosition[en,Characters[ToString[prn]]]-2]]]

a(n) = A078197(prime(n)). - Rémy Sigrist, Feb 12 2021

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

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A309343 Position of start of first occurrence of palindromic prime(n) after the decimal point in expansion of Pi.

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A341442 a(n) is the position of the start of the first occurrence of prime(n) after the decimal point in the expansion of e.

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