

A316941


The natural numbers sequence where every composite is replaced by a prime, according to the rule explained in the Comments section.


1



1, 2, 3, 211, 5, 23, 7, 2692213, 311, 773, 11, 3251, 13, 313, 1129, 3313788967, 17, 29, 19, 724553, 37, 211, 23, 2692213, 773, 3251, 313, 3313788967, 29, 3181, 31, 210527, 311, 3581, 1129, 7529, 37, 373, 313, 232357, 41, 19181, 43, 2111, 3119014487, 223, 47, 310345345771837, 31079, 3197071252784831
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OFFSET

1,2


COMMENTS

Only the composites are replaced by a prime; 1 and the primes themselves stay as they are. A composite "c" is replaced by the concatenation [az], where "a" is the smallest factor > 1 of "c" and "z" the biggest factor < "c". This transforms for instance 28 in [214] (because 2 x 14 is 28) and not in [128] (1 x 28) or [47] (4 x 7). The procedure is iterated from there until the concatenation produces a prime [214 becomes 2107, then 7301, 71043, 323681, 431751, 3143917, 7449131, 12895779, 34298593, 74899799, 135761523, 345253841, 941366901 which ends into the prime 3313788967, prime that will thus be a(28)].


LINKS

JeanMarc Falcoz, Table of n, a(n) for n = 1..175


EXAMPLE

As the first three natural numbers (1, 2 and 3) are not composites, they stay as they are. Then 4 becomes 22, and 22 produces the prime 211; 5 is a prime; 6 becomes the prime 23; 7 is a prime; 8 ends on the prime 2692213; 9 becomes 33 and 33 produces the prime 311; 10 produces the chain 25, 55, 511, 773 (prime); etc.
Some terms of this sequence are huge: a(158) is a 70digit prime, for instance.


CROSSREFS

Cf. A002808 (the composite numbers).
Sequence in context: A191835 A317550 A195264 * A037274 A321225 A037275
Adjacent sequences: A316938 A316939 A316940 * A316942 A316943 A316944


KEYWORD

base,nonn


AUTHOR

Eric Angelini and JeanMarc Falcoz, Jul 17 2018


STATUS

approved



