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%I #26 Nov 27 2022 11:37:52
%S 1,2,6,11,12,17,30,41,72,101,156,546,1481,3917,11886,14627,27737,
%T 78696,118901,137436,1676610,12618762,111018431,574060031,47357739281,
%U 168920413410
%N Integer pairs that generate only odd prime sums (as described in comment).
%C Odd terms of the pairs are prime (besides 1). Sequence is extended by adding satisfactory pairs of the next larger odd, even pair, with the odds being prime and selected first for the pair. Not every prime will be seen, limited duplicates will be seen. Seeding was 1, 2, 6, 11 and final sequence is ordered.
%C Is the sequence infinite? Similar sequences may exist beginning with different seeds and protocols, e.g., 1, 2, 3, 4, ??.
%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/2962971/compressing-the-primes-using-simple-addition">Compressing the Primes Using Simple Addition</a>
%H Bill McEachen, <a href="/A357776/a357776.txt">PARI script</a>
%e From the 4 initial seeds we see sums 1 + 2, 1 + 6, 11 + 2, 11 + 6 so 1, 2, 6 and 11 are all sequence terms. We then seek the next pair; the next available prime is 13 but as 13 + 2 yields a composite, we move to 17 as the third odd candidate. Since 17 plus each existing even is prime, we move to the next even candidate, 12. We find 12 plus each of the odds 1, 11, 17 is prime, and so the third pair added is (12, 17). Repeating, the 4th pair added is (30, 41). The 5th pair added is (72, 101), and so on. Here is the table after 4 pairs:
%e .
%e Triangle T(o,e) begins:
%e .
%e o\e| 2 6 12 30 ...
%e ---+----------------------
%e 1| 3 7 13 31 ...
%e 11| 13 17 23 41 ...
%e 17| 19 23 29 47 ...
%e 41| 43 47 53 71 ...
%e ...
%K nonn,base,more
%O 1,2
%A _Bill McEachen_, Oct 12 2022
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