A045983 Numbers k such that n or more consecutive integers starting at k have the same number of distinct prime divisors.

1, 2, 2, 2, 54, 91, 141, 141, 44360, 48919, 218972, 526095, 526095, 526095, 17233173, 127890362, 29138958036, 118968284928, 118968284928, 585927201062, 585927201062, 585927201062, 585927201062

Offset

1,2

Comments

a(n) = smallest number k such that the n numbers from k through n+k-1 have the same number of prime divisors.

a(24) > 10^12. - Donovan Johnson, Mar 29 2013

Links

Table of n, a(n) for n=1..23.

Example

a(5) = 54 as 54, 55, 56, 57, 58 all have 2 prime divisors.

Prog

(PARI) v=vector(16); n=0; c1=0; for(k=1, 127890377, c2=omega(k); if(c1==c2, n++; if(v[n]==0, v[n]=k-n+1; print(n " " v[n])), n=1; c1=c2)) /* Donovan Johnson, Mar 29 2013 */

Crossrefs

Cf. A006049, A075028, A075031.

Sequence in context: A175910 A257662 A075042 * A266713 A226745 A102384

Adjacent sequences: A045980 A045981 A045982 * A045984 A045985 A045986

Keyword

nonn

Author

David W. Wilson

Extensions

a(18)-a(23) from Donovan Johnson, Mar 29 2013

Status

approved