A260458 - OEIS

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

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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