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

1,1

Comments

k is not congruent to 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

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-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 *)

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
(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

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).

Sequence in context: A226818 A113462 A065392 * A296300 A358970 A224470

Adjacent sequences: A030454 A030455 A030456 * A030458 A030459 A030460

Keyword

nonn,base,nice

Author

Patrick De Geest

Status

approved