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 A161620 Primorial numbers of the form n^2 + n for some integer n. 2
 2, 6, 30, 210, 510510 (list; graph; refs; listen; history; text; internal format)
 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 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 * 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

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Last modified January 16 17:26 EST 2021. Contains 340206 sequences. (Running on oeis4.)