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.

A030459 Prime p concatenated with next prime is also prime.

Original entry on oeis.org

2, 31, 83, 151, 157, 167, 199, 233, 251, 257, 263, 271, 331, 353, 373, 433, 467, 509, 523, 541, 601, 653, 661, 677, 727, 941, 971, 1013, 1033, 1181, 1187, 1201, 1223, 1259, 1367, 1453, 1459, 1657, 1669, 1709, 1741, 1861, 1973, 2069, 2161
Offset: 1

Views

Author

Patrick De Geest

Keywords

Comments

Terms 157, 257, 263, 541, 1187, 1459, 2179 also belong to A030460. - Carmine Suriano, Jan 27 2011
All terms, except for the first one, must be either in A185934 or in A185935, i.e., have the same residue (mod 6) as the subsequent prime. - M. F. Hasler, Feb 06 2011

Links

Crossrefs

See A030461 for the concatenated primes.
Cf. A000720, A030460, A045533, A151799.

Programs

  • Mathematica
    Select[Prime[Range[500]],PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[ NextPrime[#]]]]]&] (* Harvey P. Dale, Jun 20 2011 *)
  • PARI
    o=2;forprime(p=3,1e4, isprime(eval(Str(o,o=p))) & print1(precprime(p-1)","))  \\ M. F. Hasler, Feb 06 2011

Formula

a(n) = A151799(A030460(n)).
A030461(n) = concat(a(n), A030460(n)) = A045533(A000720(a(n))).

A030461 Primes that are concatenations of two consecutive primes.

Original entry on oeis.org

23, 3137, 8389, 151157, 157163, 167173, 199211, 233239, 251257, 257263, 263269, 271277, 331337, 353359, 373379, 433439, 467479, 509521, 523541, 541547, 601607, 653659, 661673, 677683, 727733, 941947, 971977, 10131019
Offset: 1

Views

Author

Patrick De Geest

Keywords

Comments

Any term in the sequence (apart from the first) must be a concatenation of consecutive primes differing by a multiple of 6. - Francis J. McDonnell, Jun 26 2005

Examples

			a(2) is 3137 because 31 and 37 are consecutive primes and after concatenation 3137 is also prime. - _Enoch Haga_, Sep 30 2007

Links

Crossrefs

Cf. A030459.
Cf. A185934, A185935.
Subsequence of A045533.

Programs

  • Haskell
    a030461 n = a030461_list !! (n-1)
a030461_list = filter ((== 1) . a010051') a045533_list
-- Reinhard Zumkeller, Apr 20 2012
  • Magma
    [Seqint( Intseq(NthPrime(n+1)) cat Intseq(NthPrime(n)) ): n in [1..200 ]| IsPrime(Seqint( Intseq(NthPrime(n+1)) cat Intseq(NthPrime(n)) )) ]; // Marius A. Burtea, Mar 21 2019
  • Maple
    conc:=proc(a,b) local bb: bb:=convert(b,base,10): 10^nops(bb)*a+b end: p:=proc(n) local w: w:=conc(ithprime(n),ithprime(n+1)): if isprime(w)=true then w else fi end: seq(p(n),n=1..250); # Emeric Deutsch
  • Mathematica
    Select[Table[p=Prime[n]; FromDigits[Join[Flatten[IntegerDigits[{p,NextPrime[p]}]]]],{n,170}],PrimeQ] (* Jayanta Basu, May 16 2013 *)
  • PARI
    {digits(n) = if(n==0,[0],u=[];while(n>0,d=divrem(n,10);n=d[1];u=concat(d[2],u));u)} {m=1185;p=2;while(pKlaus Brockhaus
  • PARI
    o=2;forprime(p=3,1e4, isprime(eval(Str(o,o=p))) & print1(precprime(p-1),p",")) \\ M. F. Hasler, Feb 06 2011

Formula

A030461(n) = concat(A030459(n),A030460(n)) = A045533( A000720( A030459(n))). - M. F. Hasler, Feb 06 2011

Extensions

Edited by N. J. A. Sloane, Apr 19 2009 at the suggestion of Zak Seidov

A185938 First of a run of 3 or more consecutive primes which are congruent to 2 (mod 3).

Original entry on oeis.org

47, 167, 251, 257, 503, 557, 587, 647, 941, 971, 1097, 1181, 1217, 1361, 1493, 1499, 1889, 1901, 1907, 2063, 2393, 2399, 2411, 2441, 2897, 2957, 3191, 3797, 4007, 4073, 4373, 4391, 4397, 4451, 4457, 4673, 4679, 4691, 4871, 5081, 5237, 5261, 5297, 5351, 5381, 5387, 5801, 6257, 6311, 6317, 6857, 6911, 6971, 7001, 7079
Offset: 1

Views

Author

M. F. Hasler, Feb 06 2011

Keywords

Comments

The subsequence of terms A185935(k) such that nextprime(A185935(k))=A185935(k+1). If nextprime(a(n))=a(n+1), then a(n) is in A185941.

Links

Crossrefs

Cf. A185935, A185936, A185941.

Programs

  • Mathematica
    Select[Partition[Prime[Range[1500]], 3, 1], Mod[#, 3] == {2, 2, 2} &][[All, 1]] (* Paolo Xausa, Mar 07 2025 *)
  • PARI
    my(s=Mod([2,2,2],3), o=vector(#s), i=0); forprime( p=1,1e4, o[i++%3+1]=p; o-s || print1( o[(i+1)%3+1], ", "))
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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