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

0, 0, 0, 37, 311, 313, 317, 3319, 3323, 3329, 331, 337, 333341, 3343, 347, 353, 359, 3361, 367, 3371, 373, 379, 383, 389, 397, 333101, 333103, 33107, 3109, 33113, 3333333127, 333131, 3137, 333139, 33149, 33151, 33333333157, 3163, 3167

Offset: 1

Author

Amarnath Murthy, Nov 17 2005

Keywords

• base
• nonn

Comments

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.

a(378) has 23776 digits. - Harvey P. Dale, Aug 20 2020

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..377

Crossrefs

Cf. A114783, A114784.

Programs

Mathematica

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 *)

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

Extensions

More terms from Joshua Zucker, May 06 2006