A088577 Position of the first location of n in the digits of phi = 1.61803398874989....

5, 1, 20, 6, 12, 23, 2, 11, 4, 8, 232, 35, 122, 56, 255, 367, 1, 36, 3, 189, 20, 55, 63, 132, 79, 214, 68, 64, 52, 175, 41, 138, 182, 6, 27, 57, 29, 99, 33, 7, 106, 91, 348, 28, 59, 22, 71, 103, 16, 12, 215, 395, 67, 112, 58, 769, 31, 49, 23, 167, 69, 2, 51, 32, 300, 30, 124

Offset: 0

Author

Cino Hilliard, Nov 19 2003

Keywords

• nonn
• base

Examples

			The first 0 is in the 5th position of the digits of Phi, so 5 is the first entry in the sequence.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Constant Digit Scanning
• Eric Weisstein's World of Mathematics, Golden Ratio Digits

Crossrefs

Cf. A001622 (decimal expansion of phi).

Cf. A032445 (positions in Pi), A051238 (positions in e).

Programs

Mathematica

With[{phistr = StringDrop[ToString[N[GoldenRatio, 1000]], {2, 2}]}, Table[ StringPosition[phistr, ToString[n], 1][[1, 1]], {n, 0, 70}]] (* Harvey P. Dale, Sep 17 2011 *)

PARI

trajphidigitsd(n,m) = { default(realprecision,6000); p = (sqrt(5)+1)/2*10^5000; v = Vec(Str(p)); for(d=0,m, for(x=1,n, if(d<10, y = eval(v[x]), if(d<100, y = eval(v[x])*10 + eval(v[x+1]), if(d<1000, y = eval(v[x])*100 + eval(v[x+1])*10 + eval(v[x+2]), y = eval(v[x])*1000 + eval(v[x+1])*100 + eval(v[x+2])*10 + eval(v[x+3]) ); ); ); if(y == d,print1(x",");break); ); ) }