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

1,1

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.

Links

Table of n, a(n) for n=1..11.

Example

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.

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

Crossrefs

Cf. A090009, A145280.

Sequence in context: A128371 A175932 A370322 * A153655 A153657 A140152

Adjacent sequences: A225541 A225542 A225543 * A225545 A225546 A225547

Keyword

nonn,base

Author

Giovanni Resta, May 10 2013

Status

approved