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.

A159190 Main diagonal of array mentioned in A113941.

Original entry on oeis.org

6, 9, 1247, 1891, 29539
Offset: 1

Views

Author

Jonathan Vos Post, Apr 05 2009

Keywords

Comments

Main diagonal of array of k-gonal numbers which are also brilliant numbers.

Examples

			The array begins:
=============================================
....|.n=1.|.n=2.|.n=3.|..n=4.|..n=5.|in OEIS.|
=============================================
k=3.|...6.|..10.|...15.|...21.|....253.|A113940
k=4.|...4.|...9.|...25.|...49.|....121.|A001248
k=5.|..35.|.247.|.1247.|..2501.|..4187.|A113941
k=6.|...6.|..15.|..703.|..1891.|..2701.|new
k=7.|.403.|.697.|.2059.|.25351.|.29539.|new
=============================================
		

Crossrefs

Formula

A(k,n) = n-th brilliant number A078972 among (n+2)-gonal numbers.

A255584 Semiprimes of the form (4*n + 1)*(6*n + 1) = 24*n^2 + 10*n + 1.

Original entry on oeis.org

35, 247, 1247, 2501, 4187, 7957, 15251, 17767, 33227, 49051, 81317, 118301, 128627, 182527, 241001, 250717, 265651, 302177, 318551, 438751, 485357, 563347, 655051, 679057, 736751, 753667, 886657, 981317, 1010651, 1090987, 1163801, 1361837, 1563151
Offset: 1

Views

Author

Vincenzo Librandi, Feb 27 2015

Keywords

Comments

The first few values of n such that both n and n+1 give semiprimes in the sequence begin: 2607, 4017, 4062, 5967, 7107, 8472, 8892, ... In such cases, numbers of the form 10n+8 can always be expressed as the sum of the two primes 4n+1 and 6n+7. - Wesley Ivan Hurt, Feb 27 2015

Examples

			35 is in the sequence because 35 = 5*7 and 5, 7 are primes of the form 4*k+1 and 6*k+1 respectively.
247 is in the sequence because 247 = 13*19: both 13, 19 are primes of the form 6*k+1 and 13 also has the form 4*k+1.
		

Crossrefs

Subsequence of A245365.
Cf. A001358, A002144, A002476, A113941, A255607 (associated n).
Equals A033570(A130800). - M. F. Hasler, Dec 13 2019

Programs

  • Magma
    [(4*n+1)*(6*n+1): n in [1..300] | IsPrime(4*n+1) and IsPrime(6*n+1)];
    
  • Magma
    IsSemiprime:=func; [s: n in [1..300] | IsSemiprime(s) where s is 24*n^2+10*n+1];
    
  • Mathematica
    Select[Table[24 n^2 + 10 n + 1, {n, 300}], PrimeOmega[#] == 2 &] (* or *) f[n_] := Last /@ FactorInteger[n] == {1, 1}; Select[Array[24 #^2 + 10 # + 1 &, 300], f[#] &]
  • PARI
    for(n=1,250,if(bigomega(s=24*n^2+10*n+1)==2,print1(s,", "))) \\ Derek Orr, Feb 28 2015

Formula

a(n) = A033570(A130800(n)) = A033570(2*A255607(n)). - M. F. Hasler, Dec 13 2019
Showing 1-2 of 2 results.