A053013 Positions in decimal expansion of Pi where next prime begins.

1, 2, 7, 8, 11, 12, 14, 15, 19, 3076, 3077, 3078, 3081, 3082, 3083, 3831, 3833, 3835, 3836, 3838, 3921, 3926, 3927, 3929, 4000, 4010, 4011, 4012, 4014, 4016, 4018, 4019, 4020, 4023, 4024, 4038, 4040, 4045, 4096, 4097, 4103, 4104, 4110, 4113, 4115, 4124

Offset: 1

Author

Mark R. Diamond, Feb 22 2000

Keywords

• nonn
• base

Comments

This sequence refers to a variant of A047777 in which one does not require that all primes are distinct. See A229181 for first differences of this sequence. - M. F. Hasler, Sep 15 2013

Programs

Mathematica

A229181 = {1}; digits = Join[{{1}}, RealDigits[Pi, 10, 5000] // First // Rest]; digits //. {a:({A229181,%20lg%5D;%20%7B%7B1%7D,%20c%7D)%20;%20Join%5B%7B1%7D,%20Accumulate%5BA229181%5D%20+%201%5D%20(*%20_Jean-Fran%C3%A7ois%20Alcover">Integer..}..), b__Integer /; PrimeQ[FromDigits[{b}]], c___Integer} :> (Print[lg = {b} // Length]; AppendTo[A229181, lg]; {{1}, c}) ; Join[{1}, Accumulate[A229181] + 1] (* _Jean-François Alcover, Oct 17 2013 *)

Formula

Partial sums of A229181: a(n)=sum_{k=1...n} A229181(k). - M. F. Hasler, Sep 15 2013