A048932 Let d(n) = number of distinct primes dividing n (A001221). Find smallest t such that d(t)=d(t+1)=...=d(t+n-1) but d(t-1) and d(t+n) are not = d(t); then a(n)=t.

1, 14, 7, 2, 54, 91, 323, 141, 44360, 48919, 218972, 534078, 2699915, 526095, 17233173, 127890362, 29138958036, 146216247221, 118968284928, 2500769994070, 3157129230489, 22498525938216, 585927201062, 313978488186061, 571560399902283, 453918847597184

Offset

1,2

Comments

a(n) > 10^13 for n from 20 to 22. a(23) = 585927201062. - Donovan Johnson, Jul 30 2010

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

Links

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

Eric Weisstein's World of Mathematics, Cubic number.

Example

a(3)=7 since 7,8,9 all have d = 1 but d(6) and d(10) != 1 and this is the first run of 3.

Crossrefs

First occurrence of a run of length exactly n in A001221. Cf. A048971, A048972.

Sequence in context: A220672 A353120 A051655 * A329022 A033334 A161914

Adjacent sequences: A048929 A048930 A048931 * A048933 A048934 A048935

Keyword

nonn

Author

Enoch Haga

Extensions

More terms from Naohiro Nomoto, Jul 13 2001

a(16)-a(19) and a(23) from Donovan Johnson, Jul 30 2010

a(20)-a(22) from Toshitaka Suzuki, Mar 24 2025

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

Status

approved