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

1,1

Links

Table of n, a(n) for n=1..55.

Example

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.

Prog

(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 */

Crossrefs

Cf. A001622, A037024, A014777.

Sequence in context: A089572 A358929 A040348 * A365815 A185424 A040347

Adjacent sequences: A128047 A128048 A128049 * A128051 A128052 A128053

Keyword

base,nonn

Author

Gregory Allen, Feb 13 2007

Extensions

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

Status

approved