cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

Views

Author

Amarnath Murthy, Nov 17 2005

Keywords

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

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

A114784 Smallest prime of the form: all twos followed by prime(n). a(n) > prime(n). 0 if no such prime exists.

Original entry on oeis.org

0, 23, 0, 227, 211, 2213, 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222217, 2222219, 223, 229, 2222222222222222222222222231, 2237, 241, 2243, 22247
Offset: 1

Views

Author

Amarnath Murthy, Nov 17 2005

Keywords

Comments

Prime(n) is all zeros followed by prime(n). This is all twos followed by prime(n). Conjecture: No term is zero except a(1) = a(3) = 0.
a(6) has not been proved prime, but it is a probable prime. - Joshua Zucker, May 06 2006
The 206-digit number 222...217 is, in fact, prime, as quickly confirmed by the Magma Calculator (http://magma.maths.usyd.edu.au/calc/). - Jon E. Schoenfield, Aug 24 2009

Examples

			a(6) = 2213, as 213 is composite prime(6) = 13.

Crossrefs

Cf. A114783.

Extensions

More terms from Joshua Zucker, May 06 2006
Edited by T. D. Noe, Oct 30 2008

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

Views

Author

Amarnath Murthy, Nov 17 2005

Keywords

Comments

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

Examples

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

Crossrefs

Cf. A114783, A114784, A114785.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

Amarnath Murthy, Nov 17 2005

Keywords

Comments

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

Examples

			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

Crossrefs

Cf. A114783, A114784, A114785, A114786.

Extensions

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
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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