

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), 8789. [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 * A333508 A205569 A108204
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



