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.

A120851 Numbers n such that n is prime and is equal to the product of the first k primes minus the sum of the first k primes, for some k.

Original entry on oeis.org

193, 29989, 13082761331669749
Offset: 1

Views

Author

Carlos Alves, Jul 08 2006

Keywords

Comments

It is in the spirit of A096345 (only for 2 consecutive primes).
The corresponding values of k are 4, 6, 14, 548, 1190, ... a(4) = 2.452... * 10^1691, a(5) = 1.263... x 10^4142. - Amiram Eldar, Dec 19 2018

Examples

			193 = -(2+3+5+7)+(2*3*5*7) and 193 is prime.

Crossrefs

Cf. A096345, A096342, A120850.

Programs

  • Mathematica
    tb = {}; Do[pq = -Plus @@ Prime[Range[1, k]] + Times @@ Prime[Range[1, k]]; If[PrimeQ[pq], AppendTo[tb, pq]], {k, 1, 200}]; tb

Extensions

The next term is too large to include.

A109068 Products of two successive primes that can be partitioned in sum of three distinct primes which contain the prime divisors.

Original entry on oeis.org

15, 35, 77, 221, 899, 1517, 2021, 5183, 8633, 11663, 23707, 27221, 36863, 41989, 47053, 57599, 60491, 77837, 111547, 164009, 233273, 324899, 372091, 416021, 471953, 522713, 568507, 608351, 665831, 680621
Offset: 1

Views

Author

Giovanni Teofilatto, Aug 17 2005

Keywords

Comments

Largest prime of sum of three primes are primes of the form p*q - p - q, where p and q are two successive primes (A096345).

Examples

			a(1) = 15 because 15 = 3+5+7 with 3*5 =15;
a(2) = 35 because 35 = 5+7+23 with 5*7=35;
a(3) = 77 because 77 = 7+11+59 with 7*11=77;
a(4) = 221 because 221= 13+17+191 with 13*17=221

Crossrefs

Cf. A096345.

Programs

  • PARI
    lista(nn) = {for (n=1, nn, p = prime(n); q = prime(n+1); prd = p*q; if (isprime(prd - p - q), print1(prd, ", ")););} \\ Michel Marcus, Jun 03 2013

Formula

a(n) = A096345(n) - A001043(n).

Extensions

More terms from Michel Marcus, Jun 03 2013

A329857 Positive integers which can be represented as p*q - p - q where p and q are distinct odd primes.

Original entry on oeis.org

7, 11, 19, 23, 31, 35, 39, 43, 47, 55, 59, 63, 71, 79, 83, 87, 91, 95, 103, 107, 111, 115, 119, 131, 139, 143, 155, 159, 163, 167, 175, 179, 183, 191, 199, 203, 207, 211, 215, 219, 223, 231, 239, 251, 259, 263, 271, 275, 279, 287, 295, 299, 311, 323, 327, 331, 335, 343, 347, 351, 355, 359
Offset: 1

Views

Author

Craig J. Beisel, Nov 22 2019

Keywords

Crossrefs

Cf. A037165 (a subsequence), A046388, A091305, A096345, A137367 (subsequence with twin primes), A218862.

Programs

  • Mathematica
    Select[Range[360], {} != Solve[p*q-p-q  == # && p >q> 2, {p,q}, Primes] &] (* Giovanni Resta, Jan 16 2020 *)
  • PARI
    lim=1000; x=[]; forprime(p=3, lim/3, forprime(q=p+2, lim/3, if(setsearch(x,p*q-q-p),, x=setunion(x,[p*q-q-p])))); for(i=1, length(x), if(x[i]<(lim), print1(x[i], ", ")))
Showing 1-3 of 3 results.

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

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