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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.
0
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.
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
Sequence in context: A128371 A175932 A370322 * A153655 A153657 A140152
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, May 10 2013
STATUS
approved