A378293 a(1) = 1. For n > 1 if a(n-1) is a novel term a(n) = number of a(i); 1 <= i <= n-1 whose sum of decimal digits does not exceed A007953(a(n-1)). If a(n-1) has occurred k (>1) times, a(n) = k*a(n-1).

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 6, 12, 7, 14, 10, 20, 6, 18, 20, 40, 12, 24, 19, 25, 22, 14, 28, 29, 30, 12, 36, 30, 60, 25, 50, 20, 60, 120, 15, 30, 90, 40, 80, 38

Offset

1,3

Comments

The first condition of the definition implies that if a(n-1) is a novel term then a(n) <= n-1, with equality iff A007953(a(n-1)) >= A007953(a(i)); i = 1,2,...n-1. Only the second condition of the definition can produce a(n) > n, consequent to repeats of a(n-1).

Links

Table of n, a(n) for n=1..46.

Example

a(1) = 1 (given novel term) means a(2) = 1 since there is just one term having digit sum not exceeding 1. Since 1 has now occurred twice, a(3) = 2*1 = 2, another novel term with digit sum = 2. Since there are now 3 terms up to and including a(3) = 3 with digit sum at most 3, a(4) = 3. This pattern continues(4,5,6..) until reaching a(11) = 10, a novel term with digit sum = 1. At this point the number of terms in a(1),a(2),...a(11) having digit sum equal to at most 1 is 3, so a(12) = 3. Then since 3 has been seen twice, a(13) = 6; and so on.

Crossrefs

Cf. A007953.

Sequence in context: A351868 A325721 A079050 * A320109 A278062 A254597

Adjacent sequences: A378290 A378291 A378292 * A378294 A378295 A378296

Keyword

nonn,base,more,new

Author

David James Sycamore, Nov 22 2024

Status

approved