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 1-7 of 7 results.

A096497 Prime following n-th repunit.

Original entry on oeis.org

2, 13, 113, 1117, 11113, 111119, 1111151, 11111117, 111111113, 1111111121, 11111111113, 111111111149, 1111111111139, 11111111111123, 111111111111229, 1111111111111123, 11111111111111119, 111111111111111131, 1111111111111111171, 11111111111111111131, 111111111111111111157, 1111111111111111111189
Offset: 1

Views

Author

Labos Elemer, Jul 09 2004

Keywords

Comments

Not equal to A068693: first and 2nd terms differ.

Links

Crossrefs

Cf. A068693, A002275.

Programs

  • Mathematica
    Table[NextPrime[(10^n-1)/9], {n, 40}]
Table[NextPrime[FromDigits[PadRight[{},n,1]]],{n,30}] (* Harvey P. Dale, Aug 11 2023 *)
  • PARI
    a(n) = nextprime((10^n-1)/9 + 1); \\ Michel Marcus, May 02 2016
  • Python
    from sympy import nextprime
def A096497(n):
    return nextprime((10**n-1)//9) # Chai Wah Wu, Nov 04 2019

Formula

a(n) = A002275(n) + A096869(n) = A096498(n) + A096499(n).

A096498 Prime before n-th repunit.

Original entry on oeis.org

7, 109, 1109, 11093, 111109, 1111091, 11111101, 111111109, 1111111097, 11111111059, 111111111103, 1111111111093, 11111111111053, 111111111111053, 1111111111111039, 11111111111111107, 111111111111111091, 1111111111111111037, 11111111111111111027, 111111111111111111053, 1111111111111111111097
Offset: 2

Views

Author

Labos Elemer, Jul 09 2004

Keywords

Links

Crossrefs

Cf. A068693, A002275, A096497.

Programs

  • Maple
    seq(prevprime((10^n-1)/9), n=2..50); # Robert Israel, Nov 13 2017
  • Mathematica
    Table[NextPrime[(10^n - 1)/9, -1], {n, 2, 22}] (* updated by Michael De Vlieger, May 02 2016 *)
  • PARI
    a(n) = precprime((10^n-1)/9 - 1); \\ Michel Marcus, May 02 2016

Formula

a(n) = A002275(n) - A096870(n) = A096497(n) - A096499(n).

A086498 Rearrangement of primes such that every (2n)-th partial sum is a prime. Every (2n+1)-st term is the smallest prime which has not been included earlier.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 31, 19, 23, 29, 37, 41, 43, 47, 61, 53, 67, 59, 73, 71, 97, 79, 83, 89, 103, 101, 109, 107, 127, 113, 151, 131, 139, 137, 163, 149, 199, 157, 173, 167, 181, 179, 271, 191, 229, 193, 257, 197, 277, 211, 239, 223, 263, 227, 313, 233, 241, 251
Offset: 1

Views

Author

Amarnath Murthy, Jul 28 2003

Keywords

Links

Crossrefs

Cf. A086496, A086497, A096499.

Programs

  • Maple
    N:= 100: # to get all terms before the first term > Prime(N).
Primes:= [seq(ithprime(i),i=2..N)]: nP:= N-1: S:= 2: R:= 2:
do
  found:= false;
  for j from 1 to nP do
    if isprime(S+Primes[j]) then
      R:= R, Primes[j];
      S:= S + Primes[j];
      Primes:= subsop(j=NULL, Primes);
      nP:= nP-1;
      found:= true;
      break
    fi
  od;
  if not found or nP = 0 then break fi;
  R:= R, Primes[1];
  S:= S + Primes[1];
  Primes:= Primes[2..-1];
  nP:= nP-1;
od:
R; # Robert Israel, Aug 04 2020

Extensions

More terms from Ray Chandler, Sep 17 2003

A096870 Difference between the n-th repunit and the previous prime.

Original entry on oeis.org

4, 2, 2, 18, 2, 20, 10, 2, 14, 52, 8, 18, 58, 58, 72, 4, 20, 74, 84, 58, 14, 18, 82, 168, 28, 50, 168, 84, 8, 138, 112, 82, 2, 28, 2, 62, 34, 50, 74, 24, 8, 54, 204, 22, 428, 40, 118, 200, 72, 40, 30, 42, 284, 44, 114, 268, 80, 18, 4, 74, 142, 182, 140, 112, 214, 152, 90
Offset: 2

Views

Author

Robert G. Wilson v, Jul 12 2004

Keywords

Links

Crossrefs

Cf. A096869.

Programs

  • Maple
    f:= proc(n) local r; r:= (10^n-1)/9; r - prevprime(r) end proc:
map(f, [$2..100]); # Robert Israel, Feb 23 2017
  • Mathematica
    PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; Table[(10^n - 1)/9 - PrevPrim[(10^n - 1)/9], {n, 2, 70}]
Table[With[{ru=(10^n-1)/9},ru-NextPrime[ru,-1]],{n,2,70}] (* Harvey P. Dale, Aug 14 2011 *)

Formula

a(n) = A002275(n) - A096498(n) = A096499(n) - A096869(n).

A086496 Rearrangement of natural numbers such that every 2n-th partial sum is prime. Every (2n+1)-th term is the smallest number not included earlier.

Original entry on oeis.org

1, 2, 3, 5, 4, 8, 6, 12, 7, 11, 9, 15, 10, 14, 13, 17, 16, 20, 18, 32, 19, 21, 22, 26, 23, 25, 24, 36, 27, 33, 28, 34, 29, 31, 30, 42, 35, 43, 37, 39, 38, 46, 40, 58, 41, 47, 44, 52, 45, 51, 48, 62, 49, 63, 50, 60, 53, 59, 54, 74, 55, 57, 56, 70, 61, 77, 64, 76, 65, 79, 66, 72
Offset: 1

Views

Author

Amarnath Murthy, Jul 28 2003

Keywords

Examples

			1+2, 1+2+3+5, etc. yield primes.

Crossrefs

Cf. A086497, A086498, A096499.

Extensions

More terms from Ray Chandler, Sep 16 2003

A086497 Primes arising in A086496. a(n) = Sum {A086946(k), k = 1 to 2n}= 2n-th partial sum of A086496.

Original entry on oeis.org

3, 11, 23, 41, 59, 83, 107, 137, 173, 223, 263, 311, 359, 419, 479, 541, 601, 673, 751, 827, 911, 1009, 1097, 1193, 1289, 1399, 1511, 1621, 1733, 1861, 1973, 2099, 2237, 2377, 2521, 2659, 2797, 2953, 3109, 3257, 3433, 3607, 3779, 3947, 4127, 4327, 4507
Offset: 1

Views

Author

Amarnath Murthy, Jul 28 2003

Keywords

Crossrefs

Cf. A086496, A086498, A096499.

Extensions

More terms from Ray Chandler, Sep 16 2003

A096869 Difference between the n-th repunit and the next prime.

Original entry on oeis.org

1, 2, 2, 6, 2, 8, 40, 6, 2, 10, 2, 38, 28, 12, 118, 12, 8, 20, 60, 20, 46, 78, 6, 2, 102, 272, 80, 246, 6, 80, 102, 36, 116, 10, 36, 10, 238, 32, 20, 6, 78, 412, 88, 426, 118, 172, 48, 58, 112, 8, 56, 430, 90, 136, 240, 30, 140, 232, 162, 40, 226, 48, 116, 60, 690, 146, 210
Offset: 1

Views

Author

Robert G. Wilson v, Jul 12 2004

Keywords

Crossrefs

Cf. A096870.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Table[ NextPrim[(10^n - 1)/9] - (10^n - 1)/\ 9, {n, 70}]

Formula

a(n) = A096497(n) - A002275(n) = A096499(n) - A096870(n).
Showing 1-7 of 7 results.

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