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A103758 Numbers n such that the string 100n is the decimal expansion of a prime number. 1

%I #19 Sep 08 2022 08:45:17

%S 9,37,39,61,67,69,79,91,93,99,103,109,129,151,153,169,183,189,193,207,

%T 213,237,267,271,279,291,297,313,333,343,357,361,363,379,391,393,403,

%U 411,417,447,459,469,483,493,501,511,517,519,523,537,547,549,559,591

%N Numbers n such that the string 100n is the decimal expansion of a prime number.

%C n such that n + 10^(2+A055642(n)) is prime. - _Robert Israel_, Feb 23 2016

%H Robert Israel, <a href="/A103758/b103758.txt">Table of n, a(n) for n = 1..10000</a>

%e 9 is in the sequence because 1009 is prime.

%e 99 is in the sequence because 10099 is prime.

%e 103 is in the sequence because 100103 is prime.

%p select(n -> isprime(n + 10^(3+ilog10(n))), [$1..10^3]); # _Robert Israel_, Feb 23 2016

%t Select[Range[600],PrimeQ[FromDigits[Join[{1,0,0},IntegerDigits[#]]]]&] (* _Harvey P. Dale_, Sep 02 2020 *)

%o (Magma) [ n: n in [1..700] | IsPrime(Seqint(Intseq(n) cat [0, 0, 1])) ];

%o (Magma) [n: n in [1..600] | IsPrime(n+10^(2+#Intseq(n)))]; // _Vincenzo Librandi_, Feb 24 2016

%o (PARI) isok(n) = isprime(eval(concat(Str(100), Str(n)))); \\ _Michel Marcus_, Feb 23 2016

%Y Cf. A103603, A103602, A103601.

%K base,nonn

%O 1,1

%A _Parthasarathy Nambi_, Mar 28 2005

%E More terms from _Vincenzo Librandi_, Feb 01 2011

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Last modified May 6 02:22 EDT 2024. Contains 372290 sequences. (Running on oeis4.)