Problems & Puzzles: Puzzles

Puzzle 727. Extending the OEIS sequence A235680 Here we produce a sequence from a starting prime integer using recursively the following rules: 1) the next term of the sequence is another prime number equal to the sum of the previous prime term plus the product of the non-zero digits plus the sum of the digits, of the previous prime term in both operations. 2) The sequence stops when the last term is a composite, not included in the sequence Example: Lets start with the prime = 127. The sequence has exactly 5 prime terms, the original one and four produced: 127, 151, 163, 191, 211, [217, composite] As a matter of fact on Jan 13, 2014, I sent the following smallest initial terms for the OEIS seq A235680: a(n): 2, 191, 163, 151, 127, 1644997, 36778597, 935715673,... Almost immediately Giovanni Resta produced one more term: 50682890749. Q. Can you find a few next terms in this sequence?

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Contribution came from Giovanni Resta

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Resta wrote:

I let my program run up to 10^14 and I found the
next two terms of the sequence:

16390560362269 which produces other 9 primes:
16390579258007, 16390607834869, 16390890010427, 16390890663661,
16390936013357, 16390944280273, 16390959956747, 16394432038027,
16394437263551

and 63334172492839 which produces other 10 primes
63334313580647, 63334352771743, 63334432786841, 63334600002007, 63334600056473, 63334609854283, 63334878592907, 63336524616661, 63336575005199, 63336643895761.

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