A225544 a(n) begins the earliest chain of exactly n distinct primes such that any term in the chain equals the previous term increased by the product of its digits.

2, 29, 23, 347, 293, 239, 57487, 486193, 1725121513, 1221261395831, 28549657193411

Offset: 1

Author

Giovanni Resta, May 10 2013

Keywords

• nonn
• base

Comments

A chain ends either at a composite number, or at a prime which contains a zero, since the subsequent primes in the chain are identical.

Examples

			23 starts the earliest chain of length 3, since 23+2*3 = 29, 29+2*9 = 47 and 47+4*7 = 75, where the first 3 terms are distinct and prime, so a(3) = 23. The last distinct term in the chain starting at 1725121513 is the prime 1725980623 which contains a zero and thus generates itself.
		

Crossrefs

Cf. A090009, A145280.

Programs

Mathematica

seq = 0*Range[8]; p = 2; While[p < 500000, v = Length@ NestWhileList[# + Times @@ IntegerDigits@# &, p, PrimeQ@#2 && #1 != #2 &, 2] - 1; If[ seq[[v]] == 0, seq[[v]] = p]; p = NextPrime@p]; seq