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A023237 Numbers k such that k and 10*k + 1 are both prime. 8

%I #43 Feb 04 2024 01:10:55

%S 3,7,13,19,31,43,97,103,109,151,157,181,193,211,241,271,337,349,367,

%T 409,421,439,487,523,547,571,601,613,631,691,733,769,811,823,829,883,

%U 937,1009,1021,1033,1039,1063,1069,1117,1201,1249,1279,1291,1459,1483,1489

%N Numbers k such that k and 10*k + 1 are both prime.

%C Primes which with a 1 appended stay prime.

%C Corresponding values of 10n + 1 in A055781. - _Jaroslav Krizek_, Jul 14 2010

%C Subsequence of A024912. - _Michel Marcus_, May 21 2014

%H Vincenzo Librandi, <a href="/A023237/b023237.txt">Table of n, a(n) for n = 1..1000</a>

%p with(numtheory); for i from 1 to 500 do if isprime(10*ithprime(i)+1) then printf(`%d,`, ithprime(i)) fi: od: # _James A. Sellers_, Apr 09 2005

%t Select[Prime[Range[ 240]], PrimeQ[FromDigits[Join[IntegerDigits[ # ], {1}]]] &] (* _Robert G. Wilson v_, Apr 09 2005 *)

%t Select[Prime[Range[900]], PrimeQ[10 # + 1] &] (* _Vincenzo Librandi_, May 21 2014 *)

%o (Magma) [n: n in [0..1000] | IsPrime(n) and IsPrime(10*n+1)] // _Vincenzo Librandi_, Nov 20 2010

%o (Magma) [p: p in PrimesUpTo(1100)| IsPrime(10*p+1)]; // _Vincenzo Librandi_, May 21 2014

%Y Cf. A024912, A055781, A105435.

%K nonn,easy

%O 1,1

%A _David W. Wilson_

%E Edited by _N. J. A. Sloane_ at the suggestion of _M. F. Hasler_, Aug 24 2007

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)