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

Author

Rémy Sigrist, Dec 11 2019

Keywords

• nonn
• base

Comments

This sequence is a variant of A329428.

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program for A330356

Crossrefs

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

Programs

PARI

See Links section.

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.