Julio Cesar de la Yncera - cp's OEIS frontend

A158333 Position of number of digits increment in the sequence of powers of 3.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 133, 135

Offset: 0

Julio Cesar de la Yncera, Mar 16 2009

			For n=1 a(1)=3 since the sequence of powers of 3 is 1, 3, 9, 27, 81, 243, 729 and numbers of digits increase at position 1,3,5,...

A123384

A158333 := proc(n)
        1+floor(n/log10(3)) ;
end proc:
seq(A158333(n),n=0..20) ; # R. J. Mathar, Sep 01 2014

a[x_] := 1 + Floor[x/Log[10, 3]]; Table[a[i], {i, 0, 20}]

a(n)=1+Floor(n/Log_10(3)) = 1+A054965(n).

Indices in offset, example, and formula adjusted by R. J. Mathar, May 21 2009

More terms from Robert G. Wilson v, May 29 2009

A153030 Positions of even digits of Pi.

Original entry on oeis.org

3, 7, 8, 12, 17, 19, 20, 21, 22, 23, 24, 27, 29, 33, 34, 35, 36, 37, 42, 51, 53, 54, 55, 58, 60, 61, 64, 66, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 88, 89, 90, 93, 94, 98, 99, 102, 103, 105, 106, 107, 108, 109, 113, 114, 115, 117, 118, 119, 120

Offset: 1

Julio Cesar de la Yncera, Dec 17 2008

Cf. A000796.

Flatten[Position[ Map[If[EvenQ[ # ], "*", # ] &, RealDigits[ N[Pi, 100]][[1]]], "*"]]
Select[Range@140, EvenQ[RealDigits[Pi, 10, 140][[1, # ]]] &] (* Robert G. Wilson v, Dec 21 2008 *)

More concise Mathematica coding added and sequence extended by Robert G. Wilson v, Dec 21 2008

A153032 Positions of digits of Pi that are divisible by 3.

Original entry on oeis.org

1, 6, 8, 10, 13, 15, 16, 18, 21, 23, 25, 26, 28, 31, 33, 39, 42, 43, 44, 45, 46, 47, 51, 55, 56, 59, 63, 65, 66, 70, 72, 73, 76, 78, 80, 81, 83, 86, 87, 92, 98, 99, 101, 107, 109, 112, 116, 117, 118, 119, 122, 123, 124, 128, 129, 130, 133, 138, 143, 145, 147, 160, 165

Offset: 1

Julio Cesar de la Yncera, Dec 17 2008

Cf. A000796.

Flatten[Position[ Map[If[Divisible[ #, 3], "*", # ] &, RealDigits[ N[Pi, 100]][[1]]], "*"]]
Select[ Range@ 169, Mod[ RealDigits[Pi, 10, 169][[1, # ]], 3] == 0 &] (* Robert G. Wilson v, Dec 21 2008 *)

More concise Mathematica coding added and sequence extended by Robert G. Wilson v, Dec 21 2008

Name edited by Jon E. Schoenfield, Feb 27 2014

A153031 Positions of prime digits of Pi.

Original entry on oeis.org

1, 5, 7, 9, 10, 11, 14, 16, 17, 18, 22, 25, 26, 28, 29, 30, 32, 34, 40, 44, 47, 48, 49, 52, 54, 57, 62, 64, 65, 67, 74, 77, 84, 87, 90, 91, 92, 94, 97, 100, 103, 110, 112, 113, 115, 116, 121, 124, 131, 132, 134, 136, 137, 138, 140, 141, 142, 143, 144, 150, 157, 159, 161

Offset: 1

Julio Cesar de la Yncera, Dec 17 2008

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A000796.

Flatten[Position[ Map[If[PrimeQ[ # ], "*", # ] &, RealDigits[ N[Pi, 100]][[1]]], "*"]]
Select[ Range@ 166, PrimeQ[ RealDigits[Pi, 10, 166][[1, # ]]] &] (* Robert G. Wilson v, Dec 21 2008 *)
Flatten[Position[RealDigits[Pi,10,200][[1]],?PrimeQ]] (* _Harvey P. Dale, Mar 22 2015 *)

\p 1000
p=Vec(Str(Pi/10)); for(n=1, #p-9, if(isprime(eval(p[n+2])), print1(n", "))) \\ Jens Kruse Andersen, Jul 23 2014

a(n) = A073303(n) + 1. - Michel Marcus, May 29 2014

More concise Mathematica coding added and sequence extended by Robert G. Wilson v, Dec 21 2008

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User: Julio Cesar de la Yncera

A158333 Position of number of digits increment in the sequence of powers of 3.

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A153030 Positions of even digits of Pi.

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Mathematica

Extensions

A153032 Positions of digits of Pi that are divisible by 3.

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Programs

Mathematica

Extensions

A153031 Positions of prime digits of Pi.

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Extensions