A330356 Starting from n: as long as the decimal representation contains a prime number, replace the largest and leftmost such substring with the index of the corresponding prime number; a(n) corresponds to the final value.

0, 1, 1, 1, 4, 1, 6, 4, 8, 9, 10, 1, 1, 6, 14, 6, 16, 4, 18, 8, 10, 1, 1, 9, 14, 9, 16, 14, 18, 10, 10, 1, 1, 9, 14, 9, 16, 1, 18, 10, 40, 6, 6, 14, 44, 14, 46, 6, 48, 49, 10, 1, 1, 16, 14, 9, 16, 14, 18, 4, 60, 18, 18, 18, 64, 18, 66, 8, 68, 69, 40, 10, 6, 1

Offset

0,5

Comments

This sequence is a variant of A329428.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program for A330356

Formula

a(n) <= n with equality iff n belongs to A062115.

a(prime(k)) = a(k) for any k > 0 where prime(k) denotes the k-th prime number.

a(A007097(k)) = 1 for any k >= 0.

Example

For n = 8601:
- let pi = A000720,
- 8601 gives 8 followed by pi(601) = 8110,
- 8110 gives pi(811) followed by 0 = 1410,
- 1410 gives 1 followed by pi(41) followed by 0 = 1130,
- 1130 gives pi(113) followed by 0 = 300,
- 300 gives pi(3) followed by 00 = 200,
- 200 gives pi(2) followed by 00 = 100,
- no prime number appears in 100,
- hence a(8601) = 100.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000720, A007097, A062115, A327539, A329428.

Sequence in context: A000593 A115607 A318876 * A329428 A288469 A076717

Adjacent sequences: A330353 A330354 A330355 * A330357 A330358 A330359

Keyword

nonn,base

Author

Rémy Sigrist, Dec 11 2019

Status

approved