Same gaps pattern

 
NAME
The successive gaps between nonprime terms and the successive gaps between nonprime digits show the same pattern. Lexicographically earliest sequence of distinct nonnegative terms with this property.

DATA
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, 18, 20, 21, 13, 22, 24, 25, 26, 17, 27, 19, 28, 30, 23, 29, 31, 37, 32, 41, 43, 47, 33, 34, 53, 59, 61, 35, 36, 67, 38, 71, 39, 73, 79, 83, 40, 89, 42, 97, 101, 103, 107, 44, 45, 46, 109, 48, ...

COMMENT
This is a permutation of the nonnegative numbers. The nonprime integers and the prime numbers appear in their natural order.

EXAMPLE
The hereunder nonprime terms are in yellow
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, 18, 20, 21, 13, 22, 24, 25, 26, 17, 27, 19, 28, 30, 23, 29, 31, 37, 32, 41, 43, 47, 33, 34, 53, 59, 61, 35, 36, 67, 38, 71, 39, 73, 79, 83, 40, 89, 42, 97, 101, 103, 107, 44, 45, 46, 109, 48, ...

The above successive yellow terms are separated by 0 prime (no prime between 0 and 1), then 2 primes (between 1 and 4 we have 2 and 3), then 1 prime, (5), then 1 prime again (7), then 0, 0, 0, 0, 1(11), 0, 0, 0, 0, 1(13), 0, 0, 0, 1(17), 1(19), 0, 4, 3, 0, 3, 0, 1(67), 1(71), 3, 1(89), 4, 0, 0, 1(109), etc.

The hereunder nonprime digits are in yellow
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1 0, 12, 1 4, 1 1, 15, 1 6, 1 8, 20, 21, 13, 22, 24, 25, 26, 17, 27, 1 9, 28, 30, 23, 29, 31, 37, 32, 4 1, 43, 47, 33, 34, 53, 59, 6 1, 35, 36, 67, 38, 71, 39, 73, 79, 83, 4 0, 8 9, 42, 97, 1 0 1, 1 03, 1 07, 4 4, 45, 4 6, 1 0 9, 4 8,

The above successive yellow digits are separated by 0 prime digit (no prime digit between 0 and 1), then 2 prime digits (between the digits 1 and 4 we have 2 and 3), then 1 prime digit (5), then 1 prime digit again (7), then 0, 0, 0, 0, 1 (the 2 of 12), 0, 0, 0, 0, 1 (the 5 of 15), 0, 0, 0, 1 (the 2 of 20), 1 (the 2 of 21), 0, 4, 3, 0, 3, 0, 1 (the 2 of 28), 1 (the 3 of 30), 3, 1 (the 3 of 31), 4, 0, 0, 1 (the 3 of 43), etc.

We see that the two blue sequences are the same.
And hope this will be accepted in the OEIS.


 

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