A254787 a(n)= least initial term of n consecutive primes {p(m),..,p(m+n-1)} such that all numbers {1+p(m),..,1+p(m+n-1)} are a product of the same number k primes, where p(m) is m-th prime A000040(m).

2, 3, 139, 557, 3821, 53609, 179659, 7190917, 3599100, 16687573, 20394197, 101439558

Offset

1,1

Comments

Corresponding values of m are: 1,2,34,102,530,5462,16309,488739,3599100,308495917,20394197,101439558

Corresponding values of k are: 1,2,4,4,5,4,5,4,5,4,5,5

A023514(i=m,..,m+n-1) are of the same value.

Links

Table of n, a(n) for n=1..12.

Example

a(2)=3, because {p(2),p(3)}={3,5}, and {4,6}={2^2,2*3}, k=2;
a(3)=139, because {p(34),p(35),p(36)}={139,149,151}, and {140,150,152}={2^2*5*7,2*3*5^2,2^3*19}, k=4.

Crossrefs

Cf. A000040, A023514.

Sequence in context: A066908 A057738 A234999 * A042073 A124236 A371272

Adjacent sequences: A254784 A254785 A254786 * A254788 A254789 A254790

Keyword

nonn

Author

Zak Seidov, Feb 15 2015

Status

approved