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.

A218207 Number of n-digit primes of the form (k-1)^2 + k^2.

Original entry on oeis.org

1, 3, 6, 16, 42, 107, 286, 764, 2124, 5917, 17250, 49818, 145429
Offset: 1

Views

Author

Martin Renner, Oct 23 2012

Keywords

Crossrefs

Cf. A027861, A027862, A218208, A218209, A218211.

Programs

  • Mathematica
    n = 0; Table[cnt = 0; While[n++; p = 2*n^2 - 2*n + 1; p < 10^e, If[PrimeQ[p], cnt++]]; n--; cnt, {e, 10}] (* T. D. Noe, Oct 23 2012 *)

Formula

a(n) = A218208(n) - A218208(n-1)

A218209 Number of n-digit primes that are of the form (k-2)^2 + (k-1)^2 + k^2.

Original entry on oeis.org

2, 1, 3, 4, 12, 31, 86, 230, 681, 1934, 5634, 15772
Offset: 1

Views

Author

Martin Renner, Oct 23 2012

Keywords

Crossrefs

Cf. A027863, A027864, A218207, A218210, A218211.

Programs

Formula

a(n) = A218210(n) - A218210(n-1)

A218212 Number of primes up to 10^n that are the sum of six consecutive squares of nonnegative numbers.

Original entry on oeis.org

0, 0, 4, 14, 29, 78, 225, 632, 1716, 4726, 13482, 38627, 112051, 327426, 959254, 2829346, 8391477, 24975616, 74606489, 223523560, 671611810
Offset: 1

Views

Author

Martin Renner, Oct 23 2012

Keywords

Comments

These are primes of the form 91 + 42*k + 6*k^2.

Crossrefs

Cf. A027866, A027867, A218208, A218210, A218211.

Programs

  • Mathematica
    n = 0; cnt = 0; Table[While[n++; p = 91 + 42*n + 6*n^2; p < 10^e, If[PrimeQ[p], cnt++]]; n--; cnt, {e, 14}] (* T. D. Noe, Oct 23 2012, edited by Michael De Vlieger, Feb 18 2018 *)

Formula

a(n) = Sum_{k=1..n} A218211(k).

Extensions

a(13)-a(21) from Chai Wah Wu, Feb 12 2018
Changed terms (as A218211(2) is reverted back to 0) by Chai Wah Wu, Feb 13 2018

A218213 Number of n-digit primes representable as sums of consecutive squares.

Original entry on oeis.org

1, 4, 13, 30, 69, 187, 519, 1401, 3889, 10861, 31640, 90735
Offset: 1

Views

Author

Martin Renner, Oct 23 2012

Keywords

Comments

There are no common representations of two, three or six squares for n < 13, so
a(n) = A218207(n) + A218209(n) + A218211(n); n < 13.

Crossrefs

Cf. A027861, A027862, A027863, A027864, A027866, A027867, A218207, A218209, A218211.

Programs

  • Mathematica
    nn = 8; nMax = 10^nn; t = Table[0, {nn}]; Do[k = n; s = 0; While[s = s + k^2; s <= nMax, If[PrimeQ[s], t[[Ceiling[Log[10, s]]]]++];  k++], {n, Sqrt[nMax]}]; t (* T. D. Noe, Oct 23 2012 *)

Formula

a(n) = A218214(n) - A218213(n-1).
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.