A030457 Numbers k such that k concatenated with k+1 is prime.

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

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base
• nice

Comments

k is not congruent to 1 (mod 2), 1 (mod 3), or 4 (mod 5). - Charles R Greathouse IV, Apr 16 2012

Examples

			1213 is prime, therefore 12 is a term.
		

Links

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

Crossrefs

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

Cf. A010051, A001704, A068700 (subsequence).

Numbers k such that k concatenated with k+m is prime: this sequence (m=1), A032617 (m=2), A032618 (m=3), A032619 (m=4), A032620 (m=5), A032621 (m=6), A032622 (m=7), A032623 (m=8), A032624 (m=9).

Programs

Haskell

a030457 n = a030457_list !! (n-1)
a030457_list = filter ((== 1) . a010051' . a001704) [1..]
-- Reinhard Zumkeller, Jun 27 2015, Apr 26 2011

Magma

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

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-François 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 *)

PARI

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

Python

from sympy import isprime
def ok(n): return isprime(int(str(n)+str(n+1)))
print([k for k in range(500) if ok(k)]) # Michael S. Branicky, Apr 19 2023