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A030461 Primes that are concatenations of two consecutive primes. 22
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 (list; graph; refs; listen; history; text; internal format)
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

Zak Seidov, Table of n, a(n) for n=1..1000

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

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

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Last modified May 27 15:22 EDT 2017. Contains 287207 sequences.