A260458 Limit of gcd(PP(n) - k, PP(n) + k) as k -> oo, where PP(n) is the product of the first n primes.

1, 4, 3, 2, 5, 12, 7, 2, 3, 20, 11, 6, 13, 28, 15, 2, 17, 12, 19, 10, 21, 44, 23, 6, 5, 52, 3, 14, 29, 60, 31, 2, 33, 68, 35, 6, 37, 76, 39, 10, 41, 84, 43, 22, 15, 92, 47, 6, 7, 20, 51, 26, 53, 12, 55, 14, 57, 116, 59, 30, 61, 124, 21, 2, 65, 132, 67, 34

Offset

1,2

Comments

a(n) < n if n is in A013929 (numbers that are not squarefree);

a(n) = n if n is in A008578 (primes at beginning of 20th century);

a(n) > n if n is in A039956 (even squarefree numbers).

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

For n = 3:
k    2*3*5-k   2*3*5-k   GCD
1       29       31       1
2       28       32       4
3       27       33       3
4       26       34       2
For n = 4:
k    2*3*5*7-k   2*3*5*7-k   GCD
1       29       31           1
2       28       32           4
3       27       33           3
4       26       34           2

Mathematica

z = 120; f[n_] := f[n] = Product[Prime[k], {k, 1, n}];
t[n_, k_] := t[n, k] = GCD[f[n] - k, f[n] + k];
Table[t[50, k], {k, 1, z}]

Crossrefs

Cf. A000040.

Sequence in context: A222228 A263449 A261831 * A275958 A275957 A282539

Adjacent sequences: A260455 A260456 A260457 * A260459 A260460 A260461

Keyword

nonn,easy

Author

Clark Kimberling, Sep 17 2015

Status

approved