A145781 Least m >= 0 which when added to primorial(n) yields a square.

2, 3, 6, 15, 91, 246, 715, 3535, 21099, 95995, 175470, 4468006, 31516774, 192339970, 212951314, 5138843466, 76699112491, 103728576730, 3051100701874, 14417674958635, 245230361204214, 2296196521511806, 10940476546738414

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..630

C. Aebi and G. Cairns, Partitions of primes, Parabola 45, Issue 1 (2009); see the table on p. 5. - Jonathan Sondow, Jun 21 2012

Formula

a(n) = A216144(n)^2 - A002110(n). - Jonathan Sondow, Sep 02 2012

Example

a(1)= 4 - 2 = 2, a(2)= 9 - 2*3 = 3, a(3)= 36 - 2*3*5 = 6, a(4)= 225 - 2*3*5*7 = 15, and a(5)= 2401 - 2*3*5*7*11 = 91.

Mathematica

(IntegerPart[Sqrt[#]]+1)^2-#&/@Rest[FoldList[Times, 1, Prime[Range[30]]]]  (* Harvey P. Dale, Jan 14 2011 *)

Prog

(PARI) j=[]; for (n=1, 30, j=concat(j, (ceil(sqrt(prod(i=1, n, prime(i))))^2 -prod(i=1, n, prime(i))))); j

Crossrefs

Cf. A002110, A216144, A215658, A215659.

Sequence in context: A007364 A305857 A014627 * A351880 A109162 A215659

Adjacent sequences: A145778 A145779 A145780 * A145782 A145783 A145784

Keyword

nonn

Author

Alexander R. Povolotsky, Oct 18 2008

Extensions

Definition shortened and clarified by Jonathan Sondow, Sep 02 2012

Status

approved