

A047777


Primes seen in decimal expansion of Pi (disregarding the decimal period) contiguous, smallest and distinct.


16




OFFSET

1,1


COMMENTS

Sequence A121267 gives the number of digits of a(n) [but see also A229181 for a variant, cf. below]. The terms a(9)a(11) had been found by Chris Nash in Oct. 1999, and primality of the 3057digit term a(9) has been proved by J. K. Andersen in Sept. 2002, who also found the next 5 terms a(12)a(16) and the bound a(17) > 10^32000, cf. Rivera's web page "Problem 18".  M. F. Hasler, Aug 31 2013
There is a natural variant of the present sequence, using the same definition except for not requiring that all primes have to be distinct. That variant would have the same 3057digit prime as next term, and therefore have the same displayed terms and not justify a second entry in OEIS. However, terms beyond a(9) would be different: instead of 73, 467 and the 14650digit PRP, it would be followed by 7, 3, 467, 2, 2, and a 748digit prime. Sequence A229181 yields the size of these terms.  M. F. Hasler, Sep 15 2013


LINKS

Table of n, a(n) for n=1..8.
Joseph L. Pe, Trying to Write e as a Concatenation of Primes (2009)
C. Rivera, Prime Puzzles
Index entries related to "constant primes".


MATHEMATICA

digits = Join[{{3}}, RealDigits[Pi, 10, 4000] // First // Rest]; used = {}; primes = digits //. {a:({_Integer..}..), b__Integer /; PrimeQ[p = FromDigits[{b}]] && FreeQ[used, p], c___Integer} :> (Print[p]; AppendTo[used, p]; {a, {p}, c}); Select[primes, Head[#] == List &] // Flatten (* JeanFrançois Alcover, Oct 16 2013 *)


CROSSREFS

Cf. A053013, A000796.
Cf. A005042, A104841, A198018, A198019, A198187.
Sequence in context: A280655 A262651 A055379 * A195834 A124393 A116182
Adjacent sequences: A047774 A047775 A047776 * A047778 A047779 A047780


KEYWORD

nice,nonn,base


AUTHOR

Carlos Rivera


EXTENSIONS

The next term is the 3057digit prime formed from digits 19 through 3075. It is 846264338327950...708303906979207.  Mark R. Diamond, Feb 22 2000
The two terms after that are 73 and 467.  Jason Earls, Apr 05 2001


STATUS

approved



