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.

A099802 Bisection of A000720.

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 11, 11, 11, 12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 30, 30, 30, 30, 30, 31, 31, 32, 32, 32, 33, 34, 34, 34, 34, 34
Offset: 1

Views

Author

N. J. A. Sloane, Nov 19 2004

Keywords

Comments

Maximal number of primes possible in a string of 2n consecutive numbers. - Lekraj Beedassy, Dec 04 2004
a(n) = A139325(n,1) + 1. - Reinhard Zumkeller, Apr 14 2008
Or the number of primes <= 2n. - Juri-Stepan Gerasimov, Oct 29 2009

Crossrefs

Cf. A099081.

Programs

Formula

a(n) = A000720(n) + A035250(n) - A010051(n). - Reinhard Zumkeller, Jul 05 2010
a(n) = A000720(2*n). - Wesley Ivan Hurt, Jun 16 2013

Extensions

More terms from Emeric Deutsch, Apr 12 2005

A099082 Numbers k such that 1.2. ... .k-1.k + 2 is prime (dot between numbers means concatenation).

Original entry on oeis.org

1, 5, 9, 11, 65, 159
Offset: 1

Views

Author

Farideh Firoozbakht, Oct 23 2004

Keywords

Comments

Numbers k such that A007908(k)+2 is prime.
Next term is greater than 2000.
a(7) > 4034. - J.W.L. (Jan) Eerland, Nov 19 2022
a(7) > 15176. - J.W.L. (Jan) Eerland, Feb 24 2023
a(7) > 30000. - Michael S. Branicky, Sep 13 2024

Examples

			9 is in the sequence because 123456789 + 2 is prime.

Crossrefs

Cf. A007908, A099081, A099083.

Programs

  • Mathematica
    n=0;Monitor[Parallelize[While[True,If[PrimeQ[2+ToExpression[StringJoin[ToString/@Table[k,{k,1,n}]]]],Print[n]];n++];n],n] (* J.W.L. (Jan) Eerland, Nov 19 2022 *)

A099083 Numbers k such that 1.2. ... .k-1.k - 2 is prime (where dot between numbers means concatenation).

Original entry on oeis.org

5, 31, 103, 111, 119, 201
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 03 2004

Keywords

Comments

Each term is odd and next term is greater than 2200.
Any further terms exceed 13000. - Lucas A. Brown, Mar 06 2024
Any further terms exceed 30000. - Michael S. Branicky, Sep 13 2024

Examples

			31 is in the sequence because 12345678910111213141516171819202122232425262728293031 - 2 is prime.

Crossrefs

Cf. A099081, A099082.

A099084 Numbers k such that 1.2. ... .k-1.k + 4 is a prime (dot between numbers means concatenation).

Original entry on oeis.org

1, 3, 27, 663, 6919
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 03 2004

Keywords

Comments

Each term is odd and next term is greater than 2500. Prime corresponding to the next term has more than 8900 digits. Number of digits of primes corresponding to the four known terms of this sequence are respectively 1,3,45 & 1881.
Next term is greater than 25000. - Michael S. Branicky, Sep 12 2024

Examples

			27 is in the sequence because 123456789101112131415161718192021222324252627 + 4 is a prime.

Crossrefs

Cf. A099081, A099082, A099083.

Extensions

a(5) from Michael S. Branicky, Jun 20 2023
Showing 1-4 of 4 results.

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

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