A229181 Number of decimal digits in the variant of A047777(n) (decimal expansion of Pi cut in "prime chunks") without the restriction that all primes must be different.

1, 5, 1, 3, 1, 2, 1, 4, 3057, 1, 1, 3, 1, 1, 748, 2, 2, 1, 2, 83, 5, 1, 2, 71, 10, 1, 1, 2, 2, 2, 1, 1, 3, 1, 14, 2, 5, 51, 1, 6, 1, 6, 3, 2, 9, 1, 16, 2, 3, 43, 1, 6, 19, 1, 5, 3, 1999, 1, 1, 2, 22, 1, 3, 1, 2, 2, 1, 2, 2, 5, 1, 1, 1, 1, 4, 1, 1, 3, 7, 5, 1, 6, 4, 3, 1, 10, 7, 1, 2, 11, 2, 5, 1, 13, 1, 20, 16, 1, 9, 16

Offset: 1

Author

M. F. Hasler, Sep 15 2013

Keywords

• nonn
• base

Comments

A variant of A121267. First differences of A053013. See these two sequences for further details.

Links

• C. Rivera, Prime strings

Crossrefs

Cf. A047777, A053013, A121267, A229155.

Programs

Mathematica

A229181 = {1}; digits = Join[{{1}}, RealDigits[Pi, 10, 10^4] // First // Rest]; digits //. {a:({A229181,%20lg%5D;%20%7B%7B1%7D,%20c%7D)%20;%20A229181%20(*%20_Jean-Fran%C3%A7ois%20Alcover">Integer..}..), b__Integer /; PrimeQ[FromDigits[{b}]], c___Integer} :> (Print[lg = {b} // Length]; AppendTo[A229181, lg]; {{1}, c}) ; A229181 (* _Jean-François Alcover, Oct 17 2013 *)

PARI

default(realprecision,5000);c=Pi/10;u=[];for(k=1,9e9,ispseudoprime(c\.1^k) & !print1(k,",") & k=0*c=frac(c*10^k))

Extensions

More terms from Jean-François Alcover, Oct 17 2013