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COMMENTS
| Take some initial sequence s1 = a(1), a(2),...
then for new sequence s2 = b(1), b(2),.. we define
b(n) = n + (n-th prime in s1).
If s1 = A000027 then we clearly get A014688.
If s1 = A014688 = 3,5,8,11,16,19,24,27,32,39,42,49,54,57,62,69,76,79,86,91,94
then b(1) = 1 + 3 (because 3 is the first prime in s1)
b(2) = 2 + 5 (because 5 is the 2nd prime in s1)
b(3) = 3 + 11 (because 11 is the 3rd prime in s1)
b(4) = 4 + 19 (because 19 is the 4th prime in s1)
b(5) = 5 + 79 (because 79 is the 5th prime in s1),
resulting sequence is A139025
Repeating the same procedure we have next sequences:
A139026: 8,25,110,287,438,623,668,1291,2342,2813,3790,3863,4230,4663,4828,6377,7468
A139027: 1292,3865,4666,8973,13936,50339,57266,67597,72316,85343,110934,132941,147990
A139028:270240,375255,635282,1000695,2039428,2602013,3398274,3748771,4300120
A139029:43448724,59672019,102128690,113904945,145135734,169755139
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