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%I #6 May 31 2016 15:38:13
%S 0,1,2,3,4,5,6,7,70,71,8,72,9,17,10,11,73,12,13,74,14,15,27,16,18,19,
%T 37,20,21,22,23,24,25,26,28,29,30,31,32,33,34,35,36,38,39,40,41,42,43,
%U 44,45,46,48,49,50,51,52,53,54,55,56,58,75,59,60,61,62,63,64,65,66,68,69,80,81,82,83,84,85,86,88,89,90,91,92,93,94,95,96,98,99,100,101,102,103,107,104,105,117,106,108,109,110,111,112,113,114,115,116,118,119,120,121,122,123,124,125,126,128,129,130,131,132,76,133,134,127,135,136,138,139,140,137,141,142,143,47,144,145,146,147,148,149,150,151,152,153,154,155,156,158,159,160,161
%N The successive numbers of digits between two "7"s in the sequence are given by the sequence itself.
%C This is the lexicographically first such sequence, starting with a(1)=0, that is 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 "7" of the sequence [0,1,2,3,4,5,6,7,70]; then there is 1 digit between the next pair of "7": [70,71]; then there are 2 digits between the next pair of "7": [71,8,72]; then there are 3 digits between the next pair of "7": [72,9,17]; then there are 4 digits between the next pair of "7": [17,10,11,73,]; then there are 5 digits between the next pair of "7": [73,12,13,74]; then there are 6 digits between the next pair of "7": [74,14,15,27], etc. The quantities 0, 1, 2, 3, 4, 5, 6,... rebuild the starting sequence. The next "gap" will contain 7 digits and the next one 70.
%K nonn,base
%O 1,3
%A _Eric Angelini_ and _Lars Blomberg_, May 23 2016
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