A030461 Primes that are concatenations of two consecutive primes.

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

1,1

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

Links

Georg Fischer, Table of n, a(n) for n = 1..5720 [First 1000 terms from Zak Seidov]

Formula

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

Example

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

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 *)

Prog

(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(p<m, q=nextprime(p+1); s=""; v=digits(p); for(j=1, length(v), s=concat(s, v[j])); v=digits(q); for(j=1, length(v), s=concat(s, v[j])); if(isprime(k=eval(s)), print1(k, ", ")); p=q)} \\ Klaus 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
(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

Crossrefs

Cf. A030459.

Cf. A185934, A185935.

Subsequence of A045533.

Sequence in context: A233226 A233446 A088385 * A152521 A267692 A136363

Adjacent sequences: A030458 A030459 A030460 * A030462 A030463 A030464

Keyword

nonn,base

Author

Patrick De Geest

Extensions

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

Status

approved