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

2, 21, 3171, 31711511, 131171431471711, 16333180310678671, 11117231176912155222911, 1291718606666545569524831, 71131144716241883115716012594411, 11110111723135559111044984144653124782571

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..10.

Example

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

Mathematica

NestList[FromDigits[Flatten[IntegerDigits/@FactorInteger[#]]]&, 2, 10] (* Harvey P. Dale, Oct 16 2014 *)

Prog

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

Crossrefs

Cf. A195264, A037274.

Sequence in context: A351580 A276654 A114846 * A201973 A278737 A162393

Adjacent sequences: A195162 A195163 A195164 * A195166 A195167 A195168

Keyword

nonn,base

Author

Franklin T. Adams-Watters, Sep 14 2011

Status

approved