A045983 - OEIS

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, 313978488186061, 453918847597184, 453918847597184, 455626105596320

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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

a(28) > 2 * 10^15. - Toshitaka Suzuki, Jun 22 2025

LINKS

Table of n, a(n) for n=1..27.

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

a(24)-a(27) from Toshitaka Suzuki, Jun 22 2025

STATUS

approved