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%I #6 May 23 2016 22:04:29
%S 0,1,2,3,4,40,41,5,42,6,7,43,8,9,14,10,11,12,13,15,16,17,18,19,20,21,
%T 22,23,25,26,27,28,29,30,31,45,32,33,35,36,37,38,39,50,51,52,53,55,56,
%U 57,58,59,60,61,62,63,46,65,66,47,67,68,69,70,71,72,73,75,76,77,78,79,80,81,82,83,85,86,87,88,24,89,90,91,48,92,93,95,49,96,97,98,99,100,101,102,103,105,106,107,108,109,110,111,34,112,113,104,115,116,117,400,118,119,120,121,401,122,123,114,125,126,127,124,128,129,130,131,402,132,133,135,134,136,137,138,139,150,403,151,152,153,155,154,156
%N The successive numbers of digits between two "4"s in the sequence are given by the sequence itself.
%C This is the lexicographically first such sequence, starting with a(1)=0, that has always been extended with the smallest integer not already present in the sequence and not leading to a contradiction.
%e There are 0 digits between the first two "4" of the sequence [0,1,2,3,4,40]; then there is 1 digit between the next pair of "4": [40,41]; then there are 2 digits between the next pair of "4": [41,5,42]; then there are 3 digits between the next pair of "4": [42,6,7,43]; then there are 4 digits between the next pair of "4": [43,8,9,14]; then there are 40 digits between the next pair of "4" [14,10,11,12,13,15,16,17,18,19,20,21,22,23,25,26,27,28,29,30,31,45], etc. The quantities 0, 1, 2, 3, 4, 40,... rebuild the starting sequence.
%K nonn,base
%O 1,3
%A _Eric Angelini_ and _Lars Blomberg_, May 23 2016
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