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A161620
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Primorial numbers of the form n^2 + n for some integer n.
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2
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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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]
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FORMULA
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a(n) = A034386(A215658(n)). - Jeppe Stig Nielsen, Mar 27 2018
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EXAMPLE
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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
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MATHEMATICA
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p=1; Do[p=p*Prime[c]; f=Floor[Sqrt[p]]; If[p==f*(f+1), Print[p]], {c, 1000}]
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PROG
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(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
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CROSSREFS
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Cf. A002110, A002378, A215658, A215659.
Sequence in context: A091456 A354411 A293756 * A333508 A205569 A108204
Adjacent sequences: A161617 A161618 A161619 * A161621 A161622 A161623
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KEYWORD
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nonn,hard,more
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AUTHOR
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Daniel Tisdale, Jun 14 2009
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EXTENSIONS
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Edited by Hans Havermann, Dec 02 2010
Edited by Max Alekseyev, Dec 03 2010
Edited by Robert Gerbicz, Dec 04 2010
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STATUS
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approved
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