A032445 Number the digits of the decimal expansion of Pi: 3 is the first, 1 is the second, 4 is the third and so on; a(n) gives the starting position of the first occurrence of n.
33, 2, 7, 1, 3, 5, 8, 14, 12, 6, 50, 95, 149, 111, 2, 4, 41, 96, 425, 38, 54, 94, 136, 17, 293, 90, 7, 29, 34, 187, 65, 1, 16, 25, 87, 10, 286, 47, 18, 44, 71, 3, 93, 24, 60, 61, 20, 120, 88, 58, 32, 49, 173, 9, 192, 131, 211, 405, 11, 5, 128, 220, 21, 313, 23, 8, 118, 99, 606
Offset: 0
Examples
a(10) = 50 because the first "10" in the decimal expansion of Pi occurs at digits 50 and 51: 31415926535897932384626433832795028841971693993751058209749445923...
Links
- T. D. Noe, Table of n, a(n) for n=0..9999
- M. J. Halm, More Sequences, Mpossibilities 83, April 2003.
- Eric Weisstein's World of Mathematics, Constant Digit Scanning
- Eric Weisstein's World of Mathematics, Pi Digits
Crossrefs
Cf. A000796 (decimal expansion of Pi).
Cf. A080597 (terms from the decimal expansion of Pi which include every combination of n digits as consecutive subsequences).
Cf. A032510 (last string seen when scanning the decimal expansion of Pi until all n-digit strings have been seen).
Cf. A064467 (primes in Pi).
Programs
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Mathematica
p = ToString[FromDigits[RealDigits[N[Pi, 10^4]][[1]]]]; Do[Print[StringPosition[p, ToString[n]][[1]][[1]]], {n, 1, 100}] With[{pi=RealDigits[Pi,10,1000][[1]]},Transpose[Flatten[Table[ SequencePosition[ pi,IntegerDigits[n],1],{n,0,70}],1]][[1]]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Dec 01 2015 *) -
PARI
A032445(n)=my(L=#Str(n)); n=Mod(n, 10^L); for(k=L-1, 9e9, Pi\.1^k-n||return(k+2-L)) \\ Make sure to use sufficient realprecision, e.g. via \p999. - M. F. Hasler, Nov 16 2013
Formula
a(n) = A176341(n)+1. - M. F. Hasler, Nov 16 2013
Extensions
More terms from Simon Plouffe. Corrected by Michael Esposito and Michelle Vella (michael_esposito(AT)oz.sas.com).
More terms from Robert G. Wilson v, Oct 04 2001
Comments