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.

A280001 Semiprimes in A157752.

Original entry on oeis.org

447914738, 5726413266646343, 52858423703753671390658, 932521283899305953765183, 10051725785115560870423121293, 55198768937767543284962316423143, 668989466176542077234982864850425170016849023265359023043369141048723978
Offset: 1

Views

Author

Zak Seidov, Feb 21 2017

Keywords

Comments

Semiprimes that are the smallest integers m == p_i (mod p_(i+1)), i=1..n; p_i = i-th prime, for some n's..
Note that these are not the smallest semiprimes m == p_i (mod p_(i+1)), i=1..n.
Instead for n=9,13,17,18,20,22,41, a(n) is the smallest semiprime for the given n.

Crossrefs

Cf. A157752.

A280002 Integers n such that A157752 (n) are primes.

Original entry on oeis.org

1, 5, 10, 23, 30, 267
Offset: 1

Views

Author

Zak Seidov, Feb 21 2017

Keywords

Comments

For n=9,13,17,18,20,22,41,..., A157752(n) is a semiprime (Cf. A280001).

Crossrefs

A268491 Array T(n,k) = least integer congruent to prime(i) mod prime(i+1) for all k <= i <= k+n; n, k >= 1; read by upward diagonals.

Original entry on oeis.org

2, 8, 3, 68, 33, 5, 1118, 348, 40, 7, 2273, 2273, 271, 128, 11, 197468, 27298, 10281, 557, 115, 13, 1728998, 112383, 112383, 20005, 3209, 302, 17, 1728998, 1728998, 1728998, 666651, 87189, 5470, 226, 19, 447914738, 447914738, 16601856, 16601856, 2598191
Offset: 1

Views

Author

M. F. Hasler, Apr 14 2016

Keywords

Examples

			The array reads: (See the original post on the SeqFan list for more data.)
   n\k: 1       2        3        4        5          6          7          8
   1    2,      3,       5,       7,       11,       13,        17,        19, ...
   2    8,      33,     40,      128,      115,     302,        226,       226, ...
   3   68,     348,     271,     557,     3209,     5470,       226,      6229, ...
   4  1118,    2273,   10281,   20005,    87189,   12899,      88937,    709247 ...
   5  2273,   27298,  112383,  666651,   2598191,  874663,    9124786,  3004394 ...
   6 197468, 112383, 1728998, 16601856, 81018715, 154484096, 285307475, 34371403...
		

Crossrefs

A157752 is column k=1. - R. J. Mathar, Apr 14 2016
The first terms of A319524 are the first terms of line n=2. - Alexandra Hercilia Pereira Silva, Sep 19 2020.

Programs

  • Maple
    T := proc(n,k)
        local lrem,leval,i ;
        lrem := [] ;
        leval := [] ;
        for i from k to n+k-1 do
            lrem := [op(lrem),ithprime(i+1)] ;
            leval := [op(leval),ithprime(i)] ;
        end do:
        chrem(leval,lrem) ;
    end proc:
    seq(seq(T(d-k,k),k=1..d-1),d=2..12) ; # R. J. Mathar, Apr 14 2016
  • PARI
    T(n,k)=lift(chinese(vector(n,i,Mod(prime(k+i-1),prime(k+i)))))
    concat(vector(10,n,vector(n,j, T(n-j+1,j))))
Showing 1-3 of 3 results.