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A032445
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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.
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20
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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
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OFFSET
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0,1
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COMMENTS
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LINKS
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Eric Weisstein's World of Mathematics, Pi Digits
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FORMULA
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EXAMPLE
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a(10) = 50 because the first "10" in the decimal expansion of Pi occurs at digits 50 and 51: 31415926535897932384626433832795028841971693993751058209749445923...
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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).
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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EXTENSIONS
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More terms from Simon Plouffe. Corrected by Michael Esposito and Michelle Vella (michael_esposito(AT)oz.sas.com).
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STATUS
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approved
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