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 A195165 Starting with 2, successively concatenate the numbers in the prime factorization of a(n-1), including both the prime and its exponent. 0

%I

%S 2,21,3171,31711511,131171431471711,16333180310678671,

%T 11117231176912155222911,1291718606666545569524831,

%U 71131144716241883115716012594411,11110111723135559111044984144653124782571

%N Starting with 2, successively concatenate the numbers in the prime factorization of a(n-1), including both the prime and its exponent.

%C Unlike similar sequences, this sequence does not terminate when a prime is reached; the next term after a prime p is 10*p+1.

%e The factorization of a(2) = 21 is 3^1 * 7^1, so we concatenate 3,1,7,1 to get a(3) = 3171.

%t NestList[FromDigits[Flatten[IntegerDigits/@FactorInteger[#]]]&,2,10] (* _Harvey P. Dale_, Oct 16 2014 *)

%o (PARI) catnum(n,m,b=10)=local(p=1);while(p<=m,p*=b);n*p+m

%o anext(n,b=10)=local(fm,r);fm=factor(n);for(k=1,matsize(fm)[1],r=catnum(r,catnum(fm[k,1],fm[k,2],b),b));r

%Y Cf. A195264, A037274.

%K nonn,base

%O 1,1

%A _Franklin T. Adams-Watters_, Sep 14 2011

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Last modified June 24 05:39 EDT 2019. Contains 324318 sequences. (Running on oeis4.)