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

0,1

Comments

See A176341 for a variant counting positions starting with 0, and A232013 for a sequence based on iterations of A176341. - M. F. Hasler, Nov 16 2013

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

Formula

a(n) = A176341(n)+1. - M. F. Hasler, Nov 16 2013

Example

a(10) = 50 because the first "10" in the decimal expansion of Pi occurs at digits 50 and 51: 31415926535897932384626433832795028841971693993751058209749445923...

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 *)

Prog

(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

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).

Sequence in context: A308408 A263169 A034060 * A333128 A135088 A346496

Adjacent sequences: A032442 A032443 A032444 * A032446 A032447 A032448

Keyword

nonn,base,easy,nice

Author

Jeff Burch, Paul Simon (paulsimn(AT)microtec.net)

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

Status

approved