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A047777 Primes seen in decimal expansion of Pi (disregarding the decimal period) contiguous, smallest and distinct. 16
3, 14159, 2, 653, 5, 89, 7, 9323 (list; graph; refs; listen; history; text; internal format)
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 3057-digit 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 3057-digit 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 14650-digit PRP, it would be followed by 7, 3, 467, 2, 2, and a 748-digit 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 (* Jean-Fran├žois 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 3057-digit 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

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Last modified June 24 01:22 EDT 2018. Contains 311819 sequences. (Running on oeis4.)