|
| |
|
|
A161620
|
|
Primorial numbers of the form n^2 + n for some integer n.
|
|
2
|
| |
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Primorial numbers m such that 4m+1 is a square.
Intersection of the sequences A002110 and A002378.
If it exists, a(6) > A034386(10^11). - Max Alekseyev, Oct 23 2011
The form is n^2 + n = n(n + 1), and the values n + 1 constitute A215659. - Jeppe Stig Nielsen, Mar 27 2018
|
|
|
LINKS
|
Table of n, a(n) for n=1..5.
C. Nelson, D. E. Penney, and C. Pomerance, 714 and 715, J. Recreational Mathematics (1974) 7(2), 87-89. [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018]
|
|
|
FORMULA
|
a(n) = A034386(A215658(n)). - Jeppe Stig Nielsen, Mar 27 2018
|
|
|
EXAMPLE
|
2 = 1*2 = 2
2*3 = 2*3 = 6
2*3*5 = 5*6 = 30
2*3*5*7 = 14*15 = 210
2*3*5*7*11*13*17 = 714*715 = 510510
|
|
|
MATHEMATICA
|
p=1; Do[p=p*Prime[c]; f=Floor[Sqrt[p]]; If[p==f*(f+1), Print[p]], {c, 1000}]
|
|
|
PROG
|
(PARI) N=10^8; si=30; q=vector(si, i, nextprime(i*N)); a=vector(si, i, 1); forprime(p=2, N, for(i=1, si, a[i]=(a[i]*p)%q[i]); v=1; for(i=1, si, if(kronecker(4*a[i]+1, q[i])==-1, v=0; break)); if(v, T=1; forprime(r=2, p, T*=r); print1(T", ")))
(PARI) pr=1; forprime(p=2, , pr*=p; s=sqrtint(pr); s*(s+1)==pr&&print1(pr, ", ")) \\ Jeppe Stig Nielsen, Mar 27 2018
|
|
|
CROSSREFS
|
Cf. A002110, A002378, A215658, A215659.
Sequence in context: A294925 A091456 A293756 * A205569 A108204 A088160
Adjacent sequences: A161617 A161618 A161619 * A161621 A161622 A161623
|
|
|
KEYWORD
|
nonn,hard,more
|
|
|
AUTHOR
|
Daniel Tisdale, Jun 14 2009
|
|
|
EXTENSIONS
|
Edited by Hans Havermann, Dec 02 2010
Edited by Max Alekseyev, Dec 03 2010
Edited by Robert Gerbicz, Dec 04 2010
|
|
|
STATUS
|
approved
|
| |
|
|
