A049121 If a(n) is prime, a(n+1) = a(n) followed by a 1; if a(n) is composite, a(n+1) = concatenation of prime factors of a(n) (with multiplicity).

0, 1, 11, 111, 337, 3371, 33711, 317661, 3195573, 33134361, 313849599, 3714945219, 33412771691, 1341179350213, 7181173232711, 28979247806109, 3318731171903071, 191053757165759337, 3505114323880284323, 131572281752894106563, 1091640386973585393403

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..60

Example

a(3)=111=3*37, so a(4)=3_37=337. 337 is prime, so a(5)=337_1=3371.

Maple

a:= proc(n) option remember; `if`(n=0, 0, (t-> parse(cat(`if`(isprime(t) or
      t<2, [t, 1][], sort(map(i-> i[1]$i[2], ifactors(t)[2]))[]))))(a(n-1)))
    end:
seq(a(n), n=0..21);  # Alois P. Heinz, Apr 04 2022

Mathematica

nxt[n_]:=If[n==0||n==1||PrimeQ[n], FromDigits[Join[IntegerDigits[n], {1}]], FromDigits[Flatten[IntegerDigits/@(Table[#[[1]], {#[[2]]}]&/@ FactorInteger[n])]]]; NestList[nxt, 0, 20] (* Harvey P. Dale, May 02 2012 *)

Prog

(Python)
from itertools import count, islice
from sympy import isprime, factorint
def agen():
    yield from [0, 1]
    an = 11
    for n in count(3):
        yield an
        if isprime(an):
            an = 10*an + 1
        else:
            an = int("".join(str(p) for p in factorint(an, multiple=True)))
print(list(islice(agen(), 21))) # Michael S. Branicky, Apr 04 2022

Crossrefs

Cf. A049201, A037274, A055657.

Sequence in context: A209233 A062095 A055657 * A143573 A248039 A244204

Adjacent sequences: A049118 A049119 A049120 * A049122 A049123 A049124

Keyword

nonn,easy,base,nice

Author

Mark Alexiuk (alexiuk(AT)ee.umanitoba.ca)

Extensions

More terms from Michel ten Voorde Corrected by Harvey P. Dale, Jun 06 2000.

Status

approved