Yellow commas, pink, red, blue...


The hereunder seqs were inspired by this one – that I had completely forgotten (click on the sequence image to enlarge it):

[I think the Yellow Comma seq above shouldn't consider that the first term a(1) is "between" yellow commas. Strictly speaking, I prefer the behavior of the seqs below – and especially the Red one compared to the Yellow].

Here are the Pink Comma sequence and the Light Pink one:
Pink
« Color in pink the commas squeezed between two identical digits. The number of digits between pink commas is given by the sequence itself. This is a permutation of the natural numbers and the lexicographically earliest such sequence. »
P=1,2,3,4,5,6,7,8,19,9,91,101,10,11,12,102,20,13,14,40,15,103,30,16,17,18,80,21,22,31,23,24,25,26,104,41,...
Light pink
« Color in light pink the commas squeezed between two identical digits. The number of terms between light pink commas is given by the sequence itself. This is a permutation of the natural numbers and the lexicographically earliest such sequence. »
Lp=1,2,3,4,5,6,7,8,9,10,11,12,20,13,30,14,15,50,16,17,18,80,19,21,31,22,23,24,25,26,27,28,81,29,31,32,33,40,34,41,100,...


Next are the Gold Comma sequence and the Silver one:
Gold
« Color in gold the commas following a prime term. The number of digits between golden commas is given by the sequence itself. This is a permutation of the natural numbers and the lexicographically earliest such sequence. »
G=1,2,3,4,5,6,8,7,9,101,10,103,12,14,11,15,16,18,13,20,21,107,22,24,25,109,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50,...
Silver
« Color in silver the commas following a prime term. The number of terms between silver commas is given by the sequence itself. This is a permutation of the natural numbers and the lexicographically earliest such sequence. »
S=1,2,3,4,5,6,8,7,9,10,12,11,14,15,16,18,13,20,21,22,24,25,17,26,27,28,30,32,33,34,19,35,36,38,39,40,42,23,44,...

Next are the Red Comma sequence and the Blue one:
Red
« Color in red the commas following an odd digit. The number of digits between red commas is given by the sequence itself. This is a permutation of the natural numbers and the lexicographically earliest such sequence. »
R=1,3,2,4,5,6,7,8,10,9,12,101,14,16,11,18,20,103,22,24,26,13,28,...
Blue
« Color in blue the commas following an even term. The number of terms between blue commas is given by the sequence itself. This is a permutation of the natural numbers and the lexicographically earliest such sequence. »
B=1,2,4,3,6,5,7,9,8,11,13,10,,15,17,19,21,23,12,25,27,29,31,14,33,...

Soon in the OEIS? Might be...
Best,
É.






























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