A340063 The primes appear in their natural order and the absolute difference between two successive primes is the sum of the digits between them.

2, 1, 3, 10, 100, 5, 20, 7, 4, 11, 110, 13, 12, 1000, 17, 200, 19, 21, 10000, 23, 6, 29, 1001, 31, 14, 100000, 37, 22, 41, 1010, 43, 30, 1000000, 47, 15, 53, 24, 59, 1100, 61, 32, 10000000, 67, 40, 71, 2000, 73, 33, 79, 102, 100000000, 83, 42, 89, 8, 97, 111, 1000000000, 101, 10001, 103, 112, 107, 10010, 109

Offset: 1

Author

Eric Angelini, Dec 27 2020

Keywords

• nonn
• base

Comments

Lexicographically earliest sequence of distinct positive terms with this property. It is conjectured that the sequence is a permutation of the integers > 1.

Examples

			prime 2 + (1) = prime 3;
prime 3 + (1+0 + 1+0+0) = prime 5; (we do not put 2 between 5 and 7 as 2 is in the sequence already and not 20 as 10 is lexicographically earlier along with 100 gives the digital sum 2).
prime 5 + (2+0) = prime 7;
prime 7 + (4) = prime 11;
prime 11 + (1+1+0) = prime 13;
prime 13 + (1+2 + 1+0+0+0) = 17; etc.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..8564 (terms < 10^999; first 515 terms from Carole Dubois)

Crossrefs

Cf. A000040 (the prime numbers), A001223 (prime gaps), A052216, A052217.