[seqfan] The first differences of S are the prime numbers of S

[Eric Angelini]

Hello SeqFans,
a bit more on first differences -- help wanted!
Best,
É.

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We color in yellow the prime numbers of the sequence S; the yellow terms are also the absolute first differences of S: 
                    _                                                                                          _
S = 1, 4, 6, 25, 8, 3, 10, 21, 34, 57, 28, 65, 12, 55, 14, 45, 92, 9,  121, 18,  85, 24, 95, 16, 105, 32, 129, 2, 111, 212, ...
Diff= 3  2 19  17  5  7  11  13  23  29  37, 53, 43, 41, 31, 47, 83, 53,  59, 103, 67, 61, 71, 79,  89, 73, 97, 127, 109, ...
      *  *
The quantity of yellow terms so far in S is low because:
- we want S to be a permutation of N;
- we want S to be the lexicographically first sequence obeying all constraints; 
- we want D to be a permutation of the prime numbers.

Could someone please check the above terms and help me computing thousand more?

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Text in full yellow and black shades here:
 http://www.cetteadressecomportecinquantesignes.com/FirstDiffPrimes.htm