|
|
A246463
|
|
a(n) = min(p +- q) > 1 with p*q being equal to the n-th primorial (A002110).
|
|
0
|
|
|
5, 7, 11, 13, 17, 107, 41, 157, 1811, 1579, 18859, 95533, 17659, 1995293, 208303, 2396687, 58513111, 299808329, 3952306763, 341777053, 115405393057, 437621467859, 1009861675153, 6660853109087, 29075165225531, 418895584426457, 2371362636817019, 6889206780487667, 5258351738694673
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,1
|
|
COMMENTS
|
All terms must be odd since 2 is only represented once in the factorization of any primorial. The two divisors of different parity, p and q, must straddle the square root of the primorial.
|
|
LINKS
|
|
|
EXAMPLE
|
a(7) = 41 since the middle four divisors of 7# or 2*3*5*7*11*13*17 = 510510 are 663, 714, 715 and 770. Because the middle two only differ by 1, the next pair, 663 and 770 are used and their difference is 107.
a(8) = 41 since the middle two divisors of 8# are 3094 and 3135 which have a difference of 41.
|
|
MATHEMATICA
|
f[n_] := Block[{k = mx = 1, fi = Prime@ Range@ n, prod = Fold[Times, 1, Prime@ Range@ n], sqrt, tms}, sqrt = Floor@ Sqrt@ prod; While[k < 2^n, tms = Times @@ (fi^IntegerDigits[k, 2, n]); If[mx < tms < sqrt, mx = tms]; k++]; prod/mx - mx]; Array[f, 30, 2]
|
|
PROG
|
(PARI) a(n)=my(P=prod(i=1, n, prime(i))); forstep(k=sqrtint(P), 1, -1, if(P%k==0 && P/k-k>1, return(P/k-k))) \\ Charles R Greathouse IV, Aug 31 2014
(PARI) a(n)=my(P=prod(i=1, n, prime(i)), t); fordiv(P, d, if(P/d-d>1, t=P/d-d, return(t))) \\ Charles R Greathouse IV, Aug 31 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|