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

%I A340063 #53 Nov 04 2023 21:52:31
%S A340063 2,1,3,10,100,5,20,7,4,11,110,13,12,1000,17,200,19,21,10000,23,6,29,
%T A340063 1001,31,14,100000,37,22,41,1010,43,30,1000000,47,15,53,24,59,1100,61,
%U A340063 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
%N A340063 The primes appear in their natural order and the absolute difference between two successive primes is the sum of the digits between them.
%C A340063 Lexicographically earliest sequence of distinct positive terms with this property. It is conjectured that the sequence is a permutation of the integers > 1.
%H A340063 David A. Corneth, <a href="/A340063/b340063.txt">Table of n, a(n) for n = 1..8564</a> (terms < 10^999; first 515 terms from Carole Dubois)
%e A340063 prime 2 + (1) = prime 3;
%e A340063 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).
%e A340063 prime 5 + (2+0) = prime 7;
%e A340063 prime 7 + (4) = prime 11;
%e A340063 prime 11 + (1+1+0) = prime 13;
%e A340063 prime 13 + (1+2 + 1+0+0+0) = 17; etc.
%Y A340063 Cf. A000040 (the prime numbers), A001223 (prime gaps), A052216, A052217.
%K A340063 nonn,base
%O A340063 1,1
%A A340063 _Eric Angelini_, Dec 27 2020