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A161620 Primorial numbers of the form n^2 + n for some integer n. 0
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). [From Max Alekseyev, Oct 23 2011]

LINKS

Table of n, a(n) for n=1..5.

C. Nelson, D. E. Penney, and C. Pomerance (1974) 714 and 715, J. Recreational Mathematics 7(2), 87-89.

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", ")))

CROSSREFS

Cf. A002110, A002378.

Sequence in context: A077176 A101178 A091456 * 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

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Last modified May 23 08:43 EDT 2017. Contains 286909 sequences.