A032621 -id:A032621 - cp's OEIS frontend

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

Patrick De Geest

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

			1213 is prime, therefore 12 is a term.

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

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).

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

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

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

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 *)

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

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

A032629 Primes that are concatenations of n with n + 6.

Original entry on oeis.org

17, 1117, 1319, 1723, 2531, 3137, 3541, 4349, 6571, 7177, 8389, 95101, 97103, 101107, 125131, 127133, 137143, 151157, 155161, 157163, 161167, 163169, 167173, 187193, 197203, 203209, 205211, 211217, 217223, 221227, 223229

Offset: 1

Patrick De Geest, May 15 1998

Cf. A032611, A032621.

Edited by Charles R Greathouse IV, Apr 28 2010

A375091 First element p of sexy prime pairs (p,p+6) whose concatenation is also prime.

Original entry on oeis.org

11, 13, 17, 31, 83, 97, 101, 151, 157, 167, 223, 227, 233, 251, 257, 263, 271, 331, 353, 373, 433, 461, 541, 601, 653, 677, 727, 821, 823, 877, 941, 971, 1013, 1033, 1181, 1187, 1223, 1367, 1447, 1453, 1657, 1693, 1741, 1861, 1973, 1993, 1997, 2207, 2281, 2333, 2393, 2441

Offset: 1

James S. DeArmon, Jul 29 2024

			11 is the first term, since (11,17) are sexy primes and 1117 is also prime.
The second term is 13, since 1319 is prime.

Intersection of A023201 and A032621.

Cf. A031924, A104227, A032629.

q:= p-> andmap(isprime, [p, p+6, parse(cat(p, p+6))]):
select(q, [$2..3000])[];  # Alois P. Heinz, Aug 02 2024

Select[Prime[Range[370]], PrimeQ[#+6] && PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[#+6]]]] &] (* Stefano Spezia, Aug 03 2024 *)

isp(p) = isprime(p+6) && isprime(eval(concat(Str(p), Str(p+6))))
select(isp, primes(100)) \\ Michel Marcus, Aug 02 2024

from sympy import isprime
def ok(n): return isprime(n) and isprime(n+6) and isprime(int(str(n)+str(n+6)))
print([k for k in range(2500) if ok(k)]) # Michael S. Branicky, Aug 01 2024

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

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A032629 Primes that are concatenations of n with n + 6.

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A375091 First element p of sexy prime pairs (p,p+6) whose concatenation is also prime.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Mathematica

PARI

Python