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

1,1

Comments

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

Links

Table of n, a(n) for n=1..13.

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

Example

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.

Prog

(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

Crossrefs

Cf. A051801, A063114, A233783.

Sequence in context: A153654 A153656 A242037 * A084323 A131983 A153718

Adjacent sequences: A233689 A233690 A233691 * A233693 A233694 A233695

Keyword

nonn,base,hard,more

Author

Carlos Rivera, Dec 14 2013

Extensions

a(13) from Giovanni Resta, Dec 15 2013

Status

approved