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%I #39 Jan 01 2022 08:11:34
%S 2,23,23,239,239,239,3413,14249,524219,4167379,324550981,2589767209,
%T 346333812907
%N The smallest prime that produces a set of n primes such that every prime after the first one is equal to the previous plus the product of its nonzero digits.
%C This sequence was produced as solution to the problem 1270 of _Claudio Meller_'s website (see link).
%H Claudio Meller, <a href="http://simplementenumeros.blogspot.mx/2013/12/1270-usando-el-producto-digital-ii.html">1270 - Usando el producto digital II</a>, Números y algos mas (in Spanish).
%e For n=3, initial prime=23, set {23, 29, 47} because 23 -> 23+2*3=29 -> 29+2*9=47.
%e For n=2 to 9, the sets are
%e 23, 29;
%e 23, 29, 47;
%e 239, 293, 347, 431;
%e 239, 293, 347, 431, 443;
%e 239, 293, 347, 431, 443, 491;
%e 3413, 3449, 3881, 4073, 4157, 4297, 4801;
%e 14249, 14537, 14957, 16217, 16301, 16319, 16481, 16673;
%e 524219, 524939, 534659, 550859, 559859, 640859, 649499, 719483, 725531.
%o (PARI) checkp(p, n) = {ok = isprime(p); for (i=1, n, print1(p, ", "); digs = digits(p); np = p + prod(i=1, #digs, if (d=digs[i], d, 1)); p = np;if (i != n, ok = ok && isprime(p));); ok;} \\ _Michel Marcus_, Dec 15 2013
%Y Cf. A051801, A063114, A233783.
%K nonn,base,hard,more
%O 1,1
%A _Carlos Rivera_, Dec 14 2013
%E a(13) from _Giovanni Resta_, Dec 15 2013
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