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.

A114788 Erroneous version of A085074.

Original entry on oeis.org

3, 7, 9, 11, 55, 29, 4913, 289, 21, 23, 325, 53, 15, 46, 81, 103, 325, 191, 261, 22, 111, 47, 3625, 10201, 183, 6859, 477, 59, 1771, 311, 28629151, 34, 35, 106, 1225, 149, 39, 118, 1161, 83, 715, 173, 45, 316, 93, 283, 60625, 9409, 801, 205, 261, 107, 11125, 111
Offset: 2

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Author

Keywords

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

A085075 Smallest number a(n) == -1 (mod n) such that the prime signature of n and a(n) is the same, or 0 if no such number exists.

Original entry on oeis.org

3, 2, 0, 19, 35, 13, 343, 0, 39, 43, 275, 103, 55, 14, 0, 67, 539, 37, 99, 62, 21, 137, 2375, 49, 51, 4913, 279, 173, 2639, 61, 0, 65, 33, 34, 0, 73, 265, 38, 999, 163, 1595, 257, 175, 44, 91, 281, 29375, 0, 99, 203, 207, 211, 2375, 219, 783, 341, 57, 353, 14399, 487, 123
Offset: 2

Views

Author

Amarnath Murthy, Jul 01 2003

Keywords

Examples

			a(6) =35 = 6*6 -1 = 3*13 and 6 = 2*3 are both of prime signature p*q, where p and q are primes.

Crossrefs

Cf. A085074.

Extensions

More terms from David Wasserman, Jan 12 2005

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.
Showing 1-5 of 5 results.

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