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A030461
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Primes that are concatenations of two consecutive primes.
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22
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Georg Fischer, Table of n, a(n) for n = 1..5720 [First 1000 terms from Zak Seidov]
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FORMULA
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A030461(n) = concat(A030459(n),A030460(n)) = A045533( A000720( A030459(n))). - M. F. Hasler, Feb 06 2011
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EXAMPLE
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a(2) is 3137 because 31 and 37 are consecutive primes and after concatenation 3137 is also prime. - Enoch Haga, Sep 30 2007
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MAPLE
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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
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MATHEMATICA
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Select[Table[p=Prime[n]; FromDigits[Join[Flatten[IntegerDigits[{p, NextPrime[p]}]]]], {n, 170}], PrimeQ] (* Jayanta Basu, May 16 2013 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,base
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AUTHOR
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Patrick De Geest
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EXTENSIONS
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Edited by N. J. A. Sloane, Apr 19 2009 at the suggestion of Zak Seidov
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STATUS
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approved
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