0,2

The next such number is greater than 10^6.

Eric Weisstein's World of Mathematics, The Golden Ratio

1 is a term because the first single digit in golden ratio phi is 1.

Number 20 is a term because the 20th pair of digits in phi is 20.

(cf. phi = 1.6180339887498948482045868343656381177203...)

PhithyNumbers[m_] := Module[{cc = m(10^m)+m, sol, aa}, sol = Partition[RealDigits[GoldenRatio, 10, cc] // First, m]; Do[aa = FromDigits[sol[[i]]]; If[aa==i, Print[{i, aa}]], {i, Length[sol]}]; ] Example: PhithyNumbers[3] produces all 3-digit Phithy numbers

Cf. A001622, A109513, A109514, A117431.

Sequence in context: A007248 A117431 A159504 this_sequence A033577 A074632 A158444

Adjacent sequences: A117429 A117430 A117431 this_sequence A117433 A117434 A117435

base,more,nonn

Colin Rose (colin(AT)tri.org.au), Mar 14 2006