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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 23 06:38 EST 2022. Contains 350504 sequences. (Running on oeis4.)