A233692 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.

2, 23, 23, 239, 239, 239, 3413, 14249, 524219, 4167379, 324550981, 2589767209, 346333812907

Offset: 1

Author

Carlos Rivera, Dec 14 2013

Keywords

• nonn
• base
• hard
• more

Comments

This sequence was produced as solution to the problem 1270 of Claudio Meller's website (see link).

Examples

			For n=3, initial prime=23, set {23, 29, 47} because 23 -> 23+2*3=29 -> 29+2*9=47.
For n=2 to 9, the sets are
      23,     29;
      23,     29,     47;
     239,    293,    347,    431;
     239,    293,    347,    431,    443;
     239,    293,    347,    431,    443,    491;
    3413,   3449,   3881,   4073,   4157,   4297,   4801;
   14249,  14537,  14957,  16217,  16301,  16319,  16481,  16673;
  524219, 524939, 534659, 550859, 559859, 640859, 649499, 719483, 725531.
		

Links

• Claudio Meller, 1270 - Usando el producto digital II, Números y algos mas (in Spanish).

Crossrefs

Cf. A051801, A063114, A233783.

Programs

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

Extensions

a(13) from Giovanni Resta, Dec 15 2013