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A114785 Smallest prime of the form: all threes followed by prime(n). a(n) >prime(n). 0 if no such prime exists. 6

%I

%S 0,0,0,37,311,313,317,3319,3323,3329,331,337,333341,3343,347,353,359,

%T 3361,367,3371,373,379,383,389,397,333101,333103,33107,3109,33113,

%U 3333333127,333131,3137,333139,33149,33151,33333333157,3163,3167

%N Smallest prime of the form: all threes followed by prime(n). a(n) >prime(n). 0 if no such prime exists.

%C Prime(n) is all zeros followed by prime(n). This is all threes followed by prime(n). Conjecture: No term is zero for n > 3.

%C a(378) has 23776 digits. - _Harvey P. Dale_, Aug 20 2020

%H Alois P. Heinz, <a href="/A114785/b114785.txt">Table of n, a(n) for n = 1..377</a>

%e a(8) = 3319, as 319 is composite prime(8) = 19.

%t sp3[p_]:=Module[{k=1},While[!PrimeQ[FromDigits[Join[PadRight[ {},k,3],IntegerDigits[ p]]]],k++];FromDigits[ Join[PadRight[ {},k,3],IntegerDigits[ p]]]]; Join[{0,0,0},Table[sp3[p],{p,Prime[Range[4,40]]}]] (* _Harvey P. Dale_, Aug 19 2020 *)

%o (PARI) a(n) = {if (n <= 3, return (0)); k = 1; p = prime(n); kp = 10^length(Str(p)); pref = (10^k-1)/3; while (! isprime(res = kp*pref + p), k++; pref = (10^k-1)/3;); res;} \\ _Michel Marcus_, Sep 15 2013

%Y Cf. A114783, A114784.

%K base,nonn

%O 1,4

%A _Amarnath Murthy_, Nov 17 2005

%E More terms from _Joshua Zucker_, May 06 2006

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Last modified May 26 02:45 EDT 2022. Contains 354074 sequences. (Running on oeis4.)