Pascal's triangle with divisors
Received this today by snail mail – which gave me the idea below: I nside Pasca l ’ s triangle a term T is the sum of the two integers above it. We do that as well hereunder – but only if T is prime. If T is not prime we only keep the largest divisor of T : Examples The 5th line is 1 — 2 — 3 — 2 — 1 (instead of Pascal ’ s 1 — 4 — 6 — 4 — 1) because 2 is the largest divisor of (1+3) and 3 is the largest divisor of (3+3). The middle term of the last line is 29 as 29 is the largest divisor of (29+29); next to 29 is 15 and 15 is indeed the largest divisor of the sum (16+29). Questions The yellow color marks the appearance of a new prime: will all primes be present, sooner or later, in the triangle (37, 41 and 43 are not present above – but 47 is)? More generally: will all the naturals appear in the triangle (10, 18, 20, 21, ... are not present yet)? If we write, from top, one line after the other (and if I left no errors) we get the hereunder sequence P (for Pascal): P =
