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

Author

Patrick De Geest

Keywords

• nonn
• base

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

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

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