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

1,4

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A114783, A114784.

Sequence in context: A197340 A165373 A165292 * A061014 A130450 A271184

Adjacent sequences: A114782 A114783 A114784 * A114786 A114787 A114788

Keyword

base,nonn

Author

Amarnath Murthy, Nov 17 2005

Extensions

More terms from Joshua Zucker, May 06 2006

Status

approved