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.

A240994 Partial sums of A086505.

Original entry on oeis.org

10, 21, 44, 75, 104, 157, 230, 283, 372, 529, 602, 739, 938, 1011, 1292, 1521, 1521, 1648, 2031, 2260, 2409, 2798, 3261, 3454, 3813, 4360, 4599, 5066, 5889, 6068
Offset: 2

Views

Author

Samuel J. Erickson, Aug 06 2014

Keywords

Examples

			The second term is obtained by taking the trace of the matrix [[3,5,11],[3,7,13],[5,7,11]].

Crossrefs

Cf. A086505.

Programs

  • Maple
    Primes:= select(isprime,{seq(2*i+1,i=1..10^5)}):
T:= 3:
for n from 2 to 100 do
  R:= Primes intersect map(`+`,Primes, -2*n);
  if nops(R) < n then break fi;
  T:= T + R[n];
  A[n]:= T;
od:
seq(A[n],n=2..100); # Robert Israel, Aug 06 2014

Extensions

Entry revised by Robert Israel, Aug 07 2014 and N. J. A. Sloane, Sep 30 2014

A231608 Table whose n-th row consists of primes p such that p + 2n is also prime, read by antidiagonals.

Original entry on oeis.org

3, 3, 5, 5, 7, 11, 3, 7, 13, 17, 3, 5, 11, 19, 29, 5, 7, 11, 13, 37, 41, 3, 7, 13, 23, 17, 43, 59, 3, 5, 11, 19, 29, 23, 67, 71, 5, 7, 17, 17, 31, 53, 31, 79, 101, 3, 11, 13, 23, 19, 37, 59, 37, 97, 107, 7, 11, 13, 31, 29, 29, 43, 71, 41, 103, 137
Offset: 1

Views

Author

T. D. Noe, Nov 26 2013

Keywords

Examples

			The following sequences are read by antidiagonals
{3, 5, 11, 17, 29, 41, 59, 71, 101, 107,...}
{3, 7, 13, 19, 37, 43, 67, 79, 97, 103,...}
{5, 7, 11, 13, 17, 23, 31, 37, 41, 47,...}
{3, 5, 11, 23, 29, 53, 59, 71, 89, 101,...}
{3, 7, 13, 19, 31, 37, 43, 61, 73, 79,...}
{5, 7, 11, 17, 19, 29, 31, 41, 47, 59,...}
{3, 5, 17, 23, 29, 47, 53, 59, 83, 89,...}
{3, 7, 13, 31, 37, 43, 67, 73, 97, 151,...}
{5, 11, 13, 19, 23, 29, 41, 43, 53, 61,...}
{3, 11, 17, 23, 41, 47, 53, 59, 83, 89,...}
...

Links

Crossrefs

Cf. A001359, A023200, A023201, A023202, A023203.
Cf. A046133, A153417, A049488, A153418, A153419.
Cf. A020483 (numbers in first column).
Cf. A086505 (numbers on the diagonal).

Programs

  • Maple
    A231608 := proc(n,k)
    local j,p ;
    j := 0 ;
    p := 2;
    while j < k do
        if isprime(p+2*n ) then
            j := j+1 ;
        end if;
        if j = k then
            return p;
        end if;
        p := nextprime(p) ;
    end do:
end proc:
for n from 1 to 10 do
    for k from 1 to 10 do
        printf("%3d ",A231608(n,k)) ;
    end do;
    printf("\n") ;
end do: # R. J. Mathar, Nov 19 2014
  • Mathematica
    nn = 10; t = Table[Select[Range[100*nn], PrimeQ[#] && PrimeQ[# + 2*n] &, nn], {n, nn}]; Table[t[[n-j+1, j]], {n, nn}, {j, n}]

A246901 a(n) is the n-th smallest prime p such that p+4n is also prime.

Original entry on oeis.org

3, 5, 11, 31, 41, 23, 73, 131, 47, 97, 149, 83, 229, 167, 89, 337, 311, 167, 307, 293, 149, 499, 509, 211, 457, 509, 311, 607, 743, 211, 787, 839, 331, 877, 521, 419, 1171, 911, 421, 787, 1289, 419, 1279, 1103, 433, 1327, 1361, 619, 1123, 1103, 617, 1663, 1721, 661, 1039, 1553, 739, 2179, 2111, 599
Offset: 1

Views

Author

Zak Seidov, Nov 16 2014

Keywords

Comments

There is an array defined by: A(n,k) is the k-th smallest prime such that p+4*n is also prime (analog of A231608). It starts
3 7 13 19 37 43 67 79 97 103
3 5 11 23 29 53 59 71 89 101
5 7 11 17 19 29 31 41 47 59
3 7 13 31 37 43 67 73 97 151
3 11 17 23 41 47 53 59 83 89
5 7 13 17 19 23 29 37 43 47
3 13 19 31 43 61 73 79 103 109
5 11 29 41 47 71 107 131 149 167
5 7 11 17 23 31 37 43 47 53
3 7 13 19 31 43 61 67 73 97
a(n) = A(n,n) reads along the main diagonal of this array. - R. J. Mathar, Nov 19 2014

Links

Crossrefs

Cf. A086505.

Programs

  • PARI
    a(n) = nb=0; forprime(p=3,, if (isprime(p+4*n), nb++; if (nb==n, return (p)))); \\ Michel Marcus, Nov 16 2014
Showing 1-3 of 3 results.

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