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

1618033, 2618033988749, 42360679, 6854101, 1109, 179, 2903, 469787, 760131556174964248389559523684316960024905121133959373, 1229, 19900502499874064149, 32199689437, 5210019193, 8429

Offset

1,1

Comments

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,...

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

Links

Table of n, a(n) for n=1..14.

Eric Weisstein's World of Mathematics, Phi-Prime

Example

1618033 is the first prime found in the decimal expansion of Golden Ratio A001622, after 6 shifts to the left.
2618033988749 is the first prime found in the decimal expansion of (Golden Ratio)^2, A104457.
42360679 is the first prime found in the decimal expansion of (Golden Ratio)^3, A098317.

Maple

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:

Crossrefs

Sequence in context: A294776 A103793 A064117 * A015334 A015377 A296450

Adjacent sequences: A173425 A173426 A173427 * A173429 A173430 A173431

Keyword

nonn,base

Author

Michel Lagneau, Feb 18 2010

Extensions

Edited by R. J. Mathar, Feb 24 2010

Status

approved