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

1,1

Comments

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

Links

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

Example

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.

Crossrefs

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

Sequence in context: A366325 A203709 A270382 * A372523 A196371 A276116

Adjacent sequences: A340060 A340061 A340062 * A340064 A340065 A340066

Keyword

nonn,base

Author

Eric Angelini, Dec 27 2020

Status

approved