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 1-5 of 5 results.

A113890 Smallest prime of the form: all eights followed by prime(n). a(n)> prime(n). 0 if no such prime exists.

Original entry on oeis.org

0, 83, 0, 887, 811, 88813, 88817, 8819, 823, 829, 8831, 8837, 88888841, 88843, 88888888888888888888888888888847, 853, 859, 8861, 8867, 888871, 88873, 88888879, 883, 88888888888889, 88897, 8101, 888103, 8888107, 888109
Offset: 1

Views

Author

Amarnath Murthy, Nov 18 2005

Keywords

Comments

Prime(n) is all zeros followed by prime(n). This is all eights followed by prime(n). Conjecture: a(n) is nonzero if n > 3.

Examples

			a(4) = 887, as 87 is composite, prime(4) = 7.

Crossrefs

Cf. A113884, A114785, A113886, A113887, A085074, A114789.

Programs

  • Maple
    cat2 := proc(a,b) a*10^(max(1,ilog10(b)+1))+b ; end: A002282 := proc(n) 8*(10^n-1)/9 ; end: A113890 := proc(n) local p,a,n8 ; p := ithprime(n) ; for n8 from 1 to 120 do a := cat2(A002282(n8),p) ; if isprime(a) then return(a) ; fi ; od: RETURN(0) ; end: seq(A113890(n),n=1..35) ; # R. J. Mathar, Jan 31 2008

Extensions

More terms from R. J. Mathar, Jan 31 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

A113889 Smallest prime of the form: all sevens followed by prime(n); a(n) > prime(n); or 0 if no such prime exists.

Original entry on oeis.org

0, 73, 0, 0, 77711, 77713, 7717, 719, 7723, 77777777777777777729, 77731, 777737, 7741, 743, 77747, 7753, 7759, 761, 77777777767, 7777777777771, 773, 777777777777777777777777777777777777777777777777777777777777777779
Offset: 1

Views

Author

Amarnath Murthy, Nov 18 2005

Keywords

Comments

Prime(n) is all zeros followed by prime(n).This is all sevens followed by prime(n). Conjecture: a(n) is nonzero if n >4.
The conjecture has been verified for n<100. - Joshua Albert (jba138(AT)psu.edu), Jan 20 2006

Examples

			a(9) = 7723, as 723 is composite, prime(9) = 23.

Crossrefs

Cf. A113884, A114785, A113886, A113887, A085074.

Programs

  • Mathematica
    Join[{0,73,0,0},Flatten[Select[#,PrimeQ,1]&/@Table[FromDigits[ PadLeft[ IntegerDigits[n],i,7]],{n,Prime[Range[5,30]]},{i,IntegerLength[ n]+1, 100}]]] (* Harvey P. Dale, Nov 20 2013 *)

Extensions

More terms from Joshua Albert (jba138(AT)psu.edu), Jan 20 2006

A113891 Smallest prime of the form: all nines followed by prime(n) with a(n) > prime(n); or 0 if no such prime exists.

Original entry on oeis.org

0, 0, 0, 97, 911
Offset: 1

Views

Author

Amarnath Murthy, Nov 18 2005

Keywords

Comments

The next term is too large to include.
The sequence continues 10^1800 - 87, 999917, 919, 9923, 929, 9931, 937, 941, 9999943, 947, 953, 999959, 99961, 967, 971, ... - Sean A. Irvine, Feb 21 2010

Examples

			a(4) = 97, prime(4) = 7.

Crossrefs

Cf. A113884, A114785, A113886, A113887, A085074, A114789, A114790.

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 1-5 of 5 results.

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