cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A030469 Primes which are concatenations of three consecutive primes.

Original entry on oeis.org

5711, 111317, 171923, 313741, 414347, 8997101, 229233239, 239241251, 263269271, 307311313, 313317331, 317331337, 353359367, 359367373, 383389397, 389397401, 401409419, 409419421, 439443449, 449457461
Offset: 1

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Comments

a(n) = "p(k) p(k+1) p(k+2)" where p(k) is k-th prime
It is conjectured that sequence is infinite. - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009

Examples

			(1) 5=p(3), 7=p(4), 11=p(5) gives a(1).
(2) 7=p(4), 11=p(5), 13=p(6), but 71113 = 7 x 10159
		

References

  • Richard E. Crandall, Carl Pomerance: Prime Numbers, Springer 2005 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
  • John Derbyshire: Prime obsession, Joseph Henry Press, Washington, DC 2003 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
  • Marcus du Sautoy: Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004

Crossrefs

Programs

  • Mathematica
    Select[Table[FromDigits[Flatten[IntegerDigits/@{Prime[n],Prime[n+1],Prime[n+2]}]],{n,11000}],PrimeQ] (* Zak Seidov, Oct 16 2009 *)
    concat[{a_,b_,c_}]:=FromDigits[Flatten[IntegerDigits/@{a,b,c}]]; Select[ concat/@ Partition[ Prime[ Range[200]],3,1],PrimeQ] (* Harvey P. Dale, Sep 06 2017 *)
  • PARI
    for(i=1,999, isprime(p=eval(Str(prime(i),prime(i+1),prime(i+2)))) & print1(p," ")) \\ M. F. Hasler, Nov 10 2009

Formula

A132903 INTERSECT A000040. - R. J. Mathar, Nov 11 2009

A030997 Smallest prime which is a concatenation of n consecutive primes.

Original entry on oeis.org

2, 23, 5711, 2357, 711131719, 113127131137139149, 29313741434753, 107109113127131137139149, 211223227229233239241251257, 691701709719727733739743751757, 2329313741434753596167
Offset: 1

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Examples

			a(5) = 711131719 is the smallest prime which is the concatenation of five consecutive primes 7, 11, 13, 17 and 19.
		

Crossrefs

Cf. A030461 (primes that are concatenations of two primes), A030469 (three primes), A030473 (four primes), A086041 (five primes).

Programs

  • PARI
    for(k=1,19, for(i=0,1e9, isprime( eval( p=concat( vector( k,j,Str( prime( i+j )))))) & break); print1(p,", ")) \\ M. F. Hasler, Nov 10 2009

A167518 Least reversible prime (A007500) which is a concatenation of n consecutive primes.

Original entry on oeis.org

2, 151157, 353359367, 139149151157, 101103107109113, 704517045770459704817048770489, 97101103107109113127, 1519315199152171522715233152411525915263, 382138233833384738513853386338773881, 9319932393379341934393499371937793919397
Offset: 1

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Author

M. F. Hasler, Nov 10 2009

Keywords

Comments

Here the weaker definition of A007500 is used, but all terms > 2 known so far are also Emirps in the sense of A006567 (i.e. different from their reversal), so it is sufficient to change the first term to 13 in order to have a sequence of "true" emirps.
Is it possible to prove that all terms > 2 are in A006567?

Crossrefs

Programs

  • PARI
    for(k=1,19,for(i=0,1e9, isprime( eval( p=concat( vector( k,j,Str( prime( i+j )))))) & isprime(eval(concat(vecextract(Vec(p),"-1..1")))) & break); print1(p,", "))

Extensions

Edited by Charles R Greathouse IV, Apr 28 2010
a(9)-a(10) from Donovan Johnson, Sep 25 2011
Showing 1-3 of 3 results.