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 1-2 of 2 results.

A115947 A117965 sorted, with repetition.

Original entry on oeis.org

1, 1, 2, 4, 6, 6, 9, 12, 18, 24, 25, 25, 48, 50, 64, 75, 91, 100, 120, 168, 169, 240, 273, 306, 320, 360, 441, 550, 588, 728, 910, 979, 1156, 1224, 1365, 1365, 1728, 2184, 2352, 2475, 3025, 3029, 4410, 4704, 4895, 5278, 5712, 5880, 6426, 7921, 9150, 9504, 12852
Offset: 1

Views

Author

Roger L. Bagula, Mar 10 2006

Keywords

Crossrefs

Cf. A117965.

Programs

  • PARI
    {z=15;v=[];for(i=1,z,for(j=1,i,v=concat(v,fibonacci(i)*fibonacci(j)*binomial(i,j)))); v=vecsort(v);for(k=1,#v,print1(v[k],","));print("\nsafe up to ",fibonacci(z+1)*binomial(z+1,1))}

Extensions

Edited by N. J. A. Sloane, Mar 13 2006 and Apr 05 2006

A117962 Partial sums of hexagonal numbers with prime indices.

Original entry on oeis.org

6, 21, 66, 157, 388, 713, 1274, 1977, 3012, 4665, 6556, 9257, 12578, 16233, 20604, 26169, 33072, 40453, 49364, 59375, 69960, 82363, 96058, 111811, 130532, 150833, 171948, 194739, 218392, 243817, 275948, 310139, 347540, 386043, 430296, 475747
Offset: 1

Views

Author

Jonathan Vos Post, Apr 05 2006

Keywords

Comments

There are no prime hexagonal numbers. The n-th hexagonal number A000384(n) = n*(2*n-1) is semiprime iff both n and 2*n-1 are prime iff A000384(n) is an element of A001358 iff n is an element of A005382.

Examples

			a(4) = hexagonal(2) + hexagonal(3) + hexagonal(5) + hexagonal(7) = 6 + 15 + 45 + 91 = 157 is prime.
a(12) = 6 + 15 + 45 + 91 + 231 + 325 + 561 + 703 + 1035 + 1653 + 1891 + 2701 = 9257 is prime.
a(26) = 150833 is prime.

Links

Crossrefs

See also: A034953 Triangular numbers (A000217) with prime indices. A001248 Squares of primes. A116995 Pentagonal numbers with prime indices. A000384 Hexagonal numbers: n(2n-1). A117961 Hexagonal numbers with prime indices. A117965 Prime partial sums of hexagonal numbers with prime indices.
Cf. A000005, A000040, A000384, A001021, A034953, A001248, A116995, A117961, A117965.

Programs

  • Mathematica
    Accumulate[Table[n(2n-1),{n,Prime[Range[50]]}]] (* Harvey P. Dale, Jan 30 2014 *)

Formula

a(n) = SUM[i=1..n] A117961(i). a(n) = SUM[i=1..n] A000040(i)*(2*A000040(i)-1). a(n) = SUM[i=1..n] A000384(prime(n)). a(n) = Partial sum of number of divisors of 12^(prime(n)-1) = SUM[i=1..n] A000005(A001021(A000040(n)-1)).
Showing 1-2 of 2 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.