Terms and digits: same pattern
The hereunder three seqs (not submitted yet to the OEIS because they are too
difficult to calculate by hand) deal with patterns of primes and nonprimes (terms & digits).
Jean-Marc Falcoz was quick to help, check, correct , extend A, B and C with their respective nice graphs:
A] Terms as well as digits fit the nonprime/prime pattern; this is the lexicographically earliest injective sequence with this property [this is now A375326]:
A] = 0,2,1,3,4,5,6,7,8,29,20,31,21,59,24,71,26,79,28,263,9,283,12,13,15,17,42,43,45,47,62,67,63,83,65,97,82,131,30,293,85,139,34,307,87,151,36,313,92,179,38,317,93,421,39,347,95,431,50,367,120,383,121,397,124,503,126,547,128,563,129,587,130,593,134,743,136,787,138,797,150,2029,51,2039,54,2129,56,2131,58,2179,70,2459,74,2621,76,2659,78,2671,202,439,203,479,205,631,207,659,212,821,213,829,215,839,217,859,242,929,243,971,245,1213...
B] Terms as well as digits fit the nonprime/nonprime/prime pattern; this is the lexicographically earliest injective sequence with this property [this is now A375327]:
B = 0,1,2,4,6,3,8,9,5,10,20,13,14,21,17,16,24,43,18,26,47,40,28,67,44,30,83,46,34,97,48,36,131,12,49,7,60,38,139,15,64,29,42,66,31,45,68,59,62,69,71,63,80,79,65,81,211,39,82,11,50,85,19,51,87,41,54,92,61,56,93,89,58,95,103,84,70,151,120,121,179,124,126,421,128,129,431,130,134,439,136,138,479,150,154,631,156,158,659,159,170,821,171,174,829,176,178,839,420,424,859,426,428,929,429,430,971,434,436,1201,74,438,1249,76,450,1289,78,451,1291,200, ...
C] Terms as well as digits fit the prime/prime/nonprime; this is the lexicographically earliest injective sequence with this property [this is now A375328]:
C = 2,3,0,5,7,1,23,13,20,37,17,21,53,43,24,73,47,26,229,239,22,67,29,25,83,31,27,97,59,32,127,137,4,251,271,33,157,173,6,331,359,35,433,457,8,379,521,52,653,673,9,571,739,55,677,823,12,71,751,57,827,853,15,79,2203,28,2207,263,30,2213,283,34,2243,293,36,2267,307,38,2287,313,39,2293,317,50,2297,347,51,2347,367,54,2383,383,56,2393,397,58,2503,503,70,2543,547,74,2593,563,76,2707,587,78,2713,593,202,743,787,203,797,2027,42,2053,857,45,2137,877,62,2153,...
Merci beaucoup Jean-Marc – encore de merveilleux graphes !
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