A114784 -id:A114784 - cp's OEIS frontend

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

Amarnath Murthy, Nov 17 2005

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

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

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

Cf. A114783, A114784.

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 *)

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

More terms from Joshua Zucker, May 06 2006

A114783 Smallest prime of the form: all ones followed by prime(n). a(n) >prime(n). 0 if no such prime exists.

Original entry on oeis.org

0, 13, 0, 17, 1111111111111111111, 113, 1117, 11119, 1123, 1129, 131, 137, 11111141, 111143, 11111111111111111111111111111147, 1153, 11159, 11161, 167, 1171, 173, 179, 1111183, 1111189, 197, 11111101, 1103, 11111111111111107, 1109

Offset: 1

Amarnath Murthy, Nov 17 2005

Prime(n) is all zeros followed by prime(n). This is all ones followed by prime(n). Conjecture: No term is zero except a(1) = a(3) = 0.

			a(7) = 1117, as 117 is composite prime(8) = 17.

Cf. A114784.

spf[n_]:=Module[{x=IntegerLength[n]+1,idn=IntegerDigits[n]}, While[ !PrimeQ[ FromDigits[ PadLeft[ idn,x,1]]],x++]; FromDigits[ PadLeft[ idn,x,1]]]; Join[{0,13,0},spf/@Prime[Range[4,30]]] (* Harvey P. Dale, May 22 2014 *)

More terms from Joshua Zucker, May 06 2006

A114786 Smallest prime of the form: one or more 4's followed by prime(n) (or 0 if no such prime exists).

Original entry on oeis.org

0, 43, 0, 47, 44444444444444411, 44444444413, 44417, 419, 4423, 4444444429, 431, 444444437, 4441, 443, 4447, 44453, 44444459, 461, 467, 4444471, 444473, 479, 4483, 44444489, 44497, 44101, 444444103, 444444444444107, 444109, 444113, 4127

Offset: 1

Amarnath Murthy, Nov 17 2005

Prime(n) is all 0's followed by prime(n). a(n) is all 4's followed by prime(n). Conjecture: No term is zero for n > 3.

a(346) = 0 or a(346) > 5000, but note a(892) = 3612. - D. S. McNeil, Feb 04 2011

			a(7) = 44417, as prime(7) = 17 and both 417 and 4417 are composite.

Cf. A114783, A114784, A114785.

Table[If[n==1||n==3, 0, Select[FromDigits/@(Join[#,IntegerDigits[Prime[n]]]& /@ (Table[PadLeft[{4},k,4],{k,50}])),PrimeQ,1][[1]]],{n,35}]  (* Harvey P. Dale, Feb 03 2011 *)

More terms from Joshua Zucker, May 06 2006

Edited by Jon E. Schoenfield, May 19 2019

A114787 Smallest prime of the form: all fives followed by prime(n). a(n) >prime(n). 0 if no such prime exists.

Original entry on oeis.org

0, 53, 0, 557, 55511, 55555555555555555555555555555555555555555555555555555555555555555555513, 55555517, 5519, 523, 55529, 5531, 0, 541, 55555543, 547, 55555553, 55555559

Offset: 1

Amarnath Murthy, Nov 17 2005

Prime(n) is all zeros followed by prime(n). This is all fives followed by prime(n).
The next sequence in this progression, "Smallest prime of the form: all sixes followed by prime(n), a(n)> prime(n)", begins 0, 0, 0, 67, then (5) = 2*(10^5039 - 1)/3 - 55, a number that consists of 5037 sixes followed by 2 ones. This does not fit into the constraints of the OEIS. N. J. A. Sloane, Nov 20 2005, based on information from Hans Havermann.
The large number is quickly certified prime by PARI's APRCL test: isprime(555...513,2) -> 1. - Hagen von Eitzen, Jun 17 2009
Next term is 5*(10^184 - 1)/9 + 6, containing 184 digits, and is too large to include here. - Arkadiusz Wesolowski, Jun 03 2013

			a(5) = 55511, as 511, 5511 are composite, prime(5) = 11.
All positive numbers of the form 5*(10^k - 1)/9 - 18 have a factor in the covering set {3, 7, 13, 37}, so a(12) = 0. - _Arkadiusz Wesolowski_, Jun 03 2013

Cf. A114783, A114784, A114785, A114786.

More terms from Joshua Zucker, May 06 2006
Edited by T. D. Noe, Oct 30 2008
a(12)-a(17) from Arkadiusz Wesolowski, Jun 03 2013

cp's OEIS Frontend

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

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A114783 Smallest prime of the form: all ones followed by prime(n). a(n) >prime(n). 0 if no such prime exists.

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A114786 Smallest prime of the form: one or more 4's followed by prime(n) (or 0 if no such prime exists).

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A114787 Smallest prime of the form: all fives followed by prime(n). a(n) >prime(n). 0 if no such prime exists.

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