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The successive numbers of digits between two "5"s in the sequence are given by the sequence itself.
0

%I #5 May 23 2016 22:05:22

%S 0,1,2,3,4,5,50,51,6,52,7,8,53,9,10,54,11,12,56,13,14,16,17,18,19,20,

%T 21,22,23,24,26,27,28,29,30,31,32,33,34,36,37,38,39,15,40,41,42,43,44,

%U 46,47,48,49,60,61,62,63,64,66,67,68,69,70,71,72,73,74,76,77,25,78,79,80,57,81,82,83,84,86,87,88,89,90,91,92,93,94,96,97,98,99,100,101,102,103,104,105,106,107,35,108,109,115,110,111,112,113,114,116,117,118,119,120,121,122,123,124,126,127,128,125,129,130,131,58,132,133,134,59,136,137,138,139,140,141,142,143,144,146,147,148,149,160,161,162,163,135,164,166,167,145,168,169,170

%N The successive numbers of digits between two "5"s in the sequence are given by the sequence itself.

%C This is the lexicographically first such sequence, starting with a(1)=0, that was always 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 "5" of the sequence [0,1,2,3,4,5,50]; then there is 1 digit between the next pair of "5": [50,51]; then there are 2 digits between the next pair of "5": [51,6,52]; then there are 3 digits between the next pair of "5": [52,7,8,53]; then there are 4 digits between the next pair of "5": [53,9,10,54]; then there are 5 digits between the next pair of "5": [54,11,12,56]; then there are 50 digits between the next pair of "5": [56,13,14,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,36,37,38,39,15], etc. The quantities 0, 1, 2, 3, 4, 5, 50,... rebuild the starting sequence.

%K nonn,base

%O 1,3

%A _Eric Angelini_ and _Lars Blomberg_, May 23 2016