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A030457 Numbers n such that n concatenated with n+1 is prime. 7
2, 6, 8, 12, 36, 42, 50, 56, 62, 68, 78, 80, 90, 92, 96, 102, 108, 120, 126, 138, 150, 156, 180, 186, 188, 192, 200, 216, 242, 246, 252, 270, 276, 278, 300, 308, 312, 318, 330, 338, 342, 350, 362, 368, 378, 390, 402, 410, 416, 420, 426, 428, 432 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

n is not 1 mod 2, 1 mod 3, or 4 mod 5. - Charles R Greathouse IV, Apr 16 2012

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

E.g. 1213 is prime, therefore 12 is a term.

MAPLE

concat:=proc(a, b) local bb: bb:=nops(convert(b, base, 10)): 10^bb*a+b end proc: a:=proc(n) if isprime(concat(n, n+1))=true then n else end if end proc: seq(a(n), n=0..500); # Emeric Deutsch, Nov 23 2007

MATHEMATICA

Select[ Range[500], PrimeQ[ ToExpression[ StringJoin[ ToString[#], ToString[#+1]]]]&] (* Jean-Fran├žois Alcover, Nov 18 2011 *)

Select[Range[500], PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[ #+1]]]]&] (* Harvey P. Dale, Dec 23 2015 *)

Position[#[[1]]*10^IntegerLength[#[[2]]]+#[[2]]&/@Partition[Range[ 500], 2, 1], _?PrimeQ]//Flatten (* Harvey P. Dale, Jul 14 2019 *)

PROG

(Haskell)

a030457 n = a030457_list !! (n-1)

a030457_list = filter ((== 1) . a010051' . a001704) [1..]

-- Reinhard Zumkeller, Jun 27 2015, Apr 26 2011

(PARI) for(n=1, 10^5, if(isprime(eval(concat(Str(n), n+1))), print1(n, ", "))); /* Joerg Arndt, Apr 27 2011 */

(MAGMA) [n: n in [1..500] | IsPrime(Seqint(Intseq(n+1) cat Intseq(n)))]; // Vincenzo Librandi, Jul 23 2016

CROSSREFS

Cf. A030458, A054211, A052089, A052087, A052088.

Cf. A010051, A001704, A068700 (subsequence).

Sequence in context: A226818 A113462 A065392 * A296300 A224470 A168247

Adjacent sequences:  A030454 A030455 A030456 * A030458 A030459 A030460

KEYWORD

nonn,base,nice

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)