A096317 - OEIS

A096317

a(n) is the minimal product of the smallest prime factor of each composite number in a prime gap of 2n.

2, 12, 120, 1680, 10080, 221760, 2217600, 34594560, 345945600, 11762150400, 29059430400, 988020633600, 21736453939200, 225268704460800, 5999261287219200, 642466345122201600, 1367831573485977600

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

a(5) = 10080: 2*5 = 10. The first occurrence of a prime gap of 10 comes after 139, with the composite numbers 140,141,142,143,144,145,146,147,148 whose smallest prime factors are 2,3,2,11,2,5,2,3,2, respectively. However, their product is 15840, which is not minimal. The 6th occurrence of a prime gap of 10 comes after 409, with the composite numbers 410,411,412,413,414,415,416,417,418 having the smallest prime factors 2,3,2,7,2,5,2,3,2 respectively. Their product is 10080, which is minimal.

CROSSREFS

Cf. A096318.

Sequence in context: A326000 A245067 A052680 * A226760 A226758 A214770

Adjacent sequences: A096314 A096315 A096316 * A096318 A096319 A096320

KEYWORD

nonn

AUTHOR

Ray G. Opao, Aug 02 2004

STATUS

approved