OFFSET
1,1
COMMENTS
Primorial numbers m such that 4m+1 is a square.
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
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
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
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