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 1-3 of 3 results.

A087506 Primes in A087461.

Original entry on oeis.org

5, 13, 71, 127, 163, 197, 227, 307, 317, 409, 523, 587, 593, 761, 857, 947, 1151, 1321, 1373, 1783, 1861, 1973, 2039, 2273, 2417, 2543, 3049, 3083, 3457, 3463, 3697, 3739, 4093, 4243, 4253, 4463, 4483, 4519, 4583, 4657, 4723, 4751, 5171, 5179, 5519, 5591
Offset: 1

Views

Author

Ray Chandler, Sep 10 2003

Keywords

Comments

Primes of the form (prime(k)+prime(2k))/2.

Crossrefs

Cf. A087461.

Programs

  • Mathematica
    Select[Table[(Prime[n]+Prime[2n])/2,{n,500}],PrimeQ] (* Harvey P. Dale, May 06 2013 *)

A092390 a(n) = prime(n) + prime(2n).

Original entry on oeis.org

5, 10, 18, 26, 40, 50, 60, 72, 84, 100, 110, 126, 142, 150, 160, 184, 198, 212, 230, 244, 254, 272, 282, 312, 326, 340, 354, 370, 380, 394, 420, 442, 454, 476, 498, 510, 530, 546, 564, 582, 600, 614, 634, 650, 660, 678, 702, 726, 748, 770, 790, 808, 818, 844
Offset: 1

Views

Author

Giovanni Teofilatto, Apr 03 2004

Keywords

Examples

			a(1) = 5 because p(1)= 2 and p(2) = 3.
a(2) = 10 because p(2)= 3 and p(4) = 7.
a(3) = 18 because p(3)= 5 and p(6) = 13.

Links

Crossrefs

Cf. A000040.
Equals 2*A087461(n) for n>1.

Programs

  • Mathematica
    Table[Prime[n]+Prime[2n],{n,60}] (* Harvey P. Dale, Jan 03 2012 *)

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
Offset 1 from Seiichi Manyama, Jan 17 2020

A258934 Half the difference between the 2n-th prime and the n-th prime, starting from n=2.

Original entry on oeis.org

2, 4, 6, 9, 12, 13, 17, 19, 21, 24, 26, 30, 32, 33, 39, 40, 45, 48, 51, 54, 57, 58, 67, 66, 69, 74, 78, 81, 84, 83, 90, 90, 99, 100, 104, 108, 110, 115, 118, 121, 126, 126, 132, 133, 140, 140, 140, 147, 156, 162, 165, 168, 171, 172, 175, 175, 185, 185, 189
Offset: 2

Views

Author

Federico Provvedi, Jun 15 2015

Keywords

Comments

The differences between odd prime numbers are always even, so a(n) is well defined for n>=2.

Links

Crossrefs

Cf. A072473, A072715, A087461.

Programs

  • Magma
    [(NthPrime(2*n)-NthPrime(n))/2: n in [2..60]]; // Bruno Berselli, Jun 15 2015
  • Mathematica
    Table[(Prime[2 k] - Prime[k])/2, {k, 2, 60}]
  • Sage
    [(nth_prime(2*n)-nth_prime(n))/2 for n in (2..60)] # Bruno Berselli, Jun 15 2015

Formula

a(n) = ( prime(2*n) - prime(n) ) / 2.
a(n) = A072473(n)/2.
Showing 1-3 of 3 results.

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

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