A337096 Lexicographically earliest sequence of positive distinct terms such that the digital root of a(n) is the number of distinct prime factors of a(n+1).

1, 2, 6, 30030, 39270, 30, 42, 43890, 46410, 51870, 66, 70, 510510, 78, 53130, 102, 105, 62790, 66990, 110, 10, 3, 114, 67830, 71610, 72930, 130, 210, 138, 154, 5, 2310, 79170, 81510, 82110, 165, 170, 9699690, 174, 182, 14, 2730, 186, 84630, 190, 7, 570570, 85470, 91770, 94710, 195, 98670

Offset

1,2

Comments

All prime numbers are present and appear in their natural order; they follow a term with digital root 1.

Links

Carole Dubois, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 with DR (digital root) = 1 and a(2) = 2 has indeed only 1 prime factor;
a(2) = 2 with DR = 2 and a(3) = 6 has indeed 2 distinct prime factors (2 and 3);
a(3) = 6 with DR = 6 and a(4) = 30030 has indeed 6 distinct prime factors (2,3,5,7,11,13);
a(4) = 30030 with DR = 6 and a(5) = 39270 has indeed 6 distinct prime factors (2,3,5,7,11,17);
a(5) = 39270 with DR = 3 and a(6) = 30 has indeed 3 distinct prime factors (2,3,5); etc.

Crossrefs

Cf. A010888.

Sequence in context: A055698 A121167 A115658 * A005607 A184391 A161563

Adjacent sequences: A337093 A337094 A337095 * A337097 A337098 A337099

Keyword

nonn,base

Author

Eric Angelini and Carole Dubois, Aug 15 2020

Status

approved