The nature of the code given in the following examples is explained in the index document.
Many interesting integer sequences can be derived from prime numbers.
The calculations given below explore such derivations.
This sequence is in the Encyclopedia as the appropriately early
A000040 (unfortunately, 40 isn't prime!).
The two simplest derivations from these are the first differences,
and half the first differences (dropping 2, the first prime).
These sequences are
A001223 and
A028334, respectively.
Analogous to these are the first sums,
and half the first sums (dropping 2, the first prime).
The second of these sequences is
A024675,
described as the average of two consecutive odd primes, being sometimes called interprimes.
The interesting thing about the interprimes is their unprimeness.
Simply Primes
The starting point for the next few sequences is the prime numbers
themselves.
p: i.20 NB. the first twenty
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
fdp =: 2&(-~/\p:) NB. first difference of primes
fdp i.21 NB. the first twenty
1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2
-:fdp>:i.21 NB. the first twenty
1 1 2 1 2 1 2 3 1 3 2 1 2 3 3 1 3 2 1 3
2+/\p: i.21 NB. the first twenty
5 8 12 18 24 30 36 42 52 60 68 78 84 90 100 112 120 128 138 144
-:2+/\p:>:i.21 NB. the first twenty
4 6 9 12 15 18 21 26 30 34 39 42 45 50 56 60 64 69 72 76