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The successive numbers of digits visible between two prime terms are given by the sequence itself.
0

%I #3 Jun 02 2016 16:09:44

%S 0,1,2,3,4,5,6,8,7,9,10,11,12,14,13,15,100,17,16,18,20,19,21,22,24,25,

%T 23,26,27,102,29,28,30,32,104,31,33,34,35,36,38,37,39,40,42,44,105,41,

%U 45,46,48,49,50,51,43,52,54,55,56,57,58,60,47,62,63,64,65,66,106,53,68,69,70,72,74,75,108,59,76,77,78,80,81,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,110,111,112,114,115,116,117,118,119,120,121,122,123,124,125,126,128,129,130,132,61

%N The successive numbers of digits visible between two prime terms are given by the sequence itself.

%C The sequence starts with a(1)=0. It is then extended with the smallest integer not yet present and not leading to a contradiction.

%e The first two primes that appear in the sequence are 2 and 3; between 2 and 3 there are 0 digits and this 0 corresponds to the starting 0 of the sequence.

%e The next prime is 5 and between 3 and 5 there is 1 digit [which is 4] and this 1 corresponds to the next term of the sequence.

%e The next prime is 7 and between 5 and 7 there are 2 digits [which are 6 and 8] and this 2 corresponds to the next term of the sequence.

%e The next prime is 11 and between 7 and 11 there are 3 digits [which are 9, 1 and 0] and this 3 corresponds to the next term of the sequence.

%e The next prime is 13 and between 11 and 13 there are 4 digits [which are 1, 2, 1 and 4] and this 4 corresponds to the next term of the sequence.

%e The next prime is 17 and between 13 and 17 there are 5 digits [which are 1, 5, 1, 0 and 0] and this 5 corresponds to the next term of the sequence.

%e Etc.

%K nonn,base

%O 1,3

%A _Eric Angelini_, Jun 01 2016