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A037000
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Positions of the digit '1' in the decimal expansion of Pi.
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37
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1, 3, 37, 40, 49, 68, 94, 95, 103, 110, 138, 148, 153, 154, 155, 163, 168, 174, 175, 198, 206, 220, 238, 243, 246, 250, 269, 281, 295, 297, 314, 319, 324, 342, 344, 362, 363, 381, 385, 390, 393, 395, 396, 417, 424, 427, 428, 432, 437, 438, 442, 445, 446
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OFFSET
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1,2
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COMMENTS
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"Positions" are indices n of digits d(n) such that Pi = Sum_{n >= 0} d(n)/10^n; see A053745 for the variant where the initial digit 3 is at position 1.
The first few primes in this sequence are 3, 37, 103, 163, 269, 281, 499, 541, 547, 587, 607, 709, 797, 859, 887, 971, 983, 997, ... (End)
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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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Conjecturally, a(n) ~ 10n.
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MAPLE
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P:= convert(evalf[100000](Pi), string)[3..-1]:
select(t -> P[t]="1", [$1..length(P)-1]); # Robert Israel, Dec 22 2013
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MATHEMATICA
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Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 1] (* Robert G. Wilson v, Mar 07 2011 *)
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PROG
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(PARI) A037000_upto(N=500, d=1)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 28 2024
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)
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STATUS
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approved
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