

A087712


a(1) = 1; if n = kth prime, a(n) = k; otherwise write all prime factors of n in nondecreasing order, replace each prime with its rank, and concatenate the ranks.


12



1, 1, 2, 11, 3, 12, 4, 111, 22, 13, 5, 112, 6, 14, 23, 1111, 7, 122, 8, 113, 24, 15, 9, 1112, 33, 16, 222, 114, 10, 123, 11, 11111, 25, 17, 34, 1122, 12, 18, 26, 1113, 13, 124, 14, 115, 223, 19, 15, 11112, 44, 133, 27, 116, 16, 1222, 35, 1114, 28, 110, 17, 1123, 18
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OFFSET

1,3


COMMENTS

Concatenations of consecutive entries of A112798.  R. J. Mathar, Feb 09 2009
The old entry with this Anumber was a duplicate of A082467.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


EXAMPLE

n = 2 = first prime, a(2) = 1.
n = 3 = second prime, a(3) = 2.
n = 4 = 2*2 > 1,1 > 11, so a(4) = 11.
n = 6 = 2*3 > 1,2 > 12, so a(6) = 12.
n = 12 = 2*2*3 > 1,1,2 > 112, so a(12) = 112.


MAPLE

# Maple program from R. J. Mathar, Feb 08 2009: (Start)
cat2 := proc(a, b) a*10^(max(1, ilog10(b)+1))+b ; end:
A049084 := proc(p) if isprime(p) then numtheory[pi](p) ; else 0 ; fi; end:
A087712 := proc(n) local pf, a, p, ex ; if isprime(n) then A049084(n) ; elif n = 1 then 1 ; else pf := ifactors(n)[2] ; a := 0 ; for p in pf do for ex from 1 to op(2, p) do a := cat2(a, A049084(op(1, p)) ) ; od: od: fi; end:
seq(A087712(n), n=1..140); # (End)
# (Maple program from David Applegate and N. J. A. Sloane, Feb 09 2009)
with(numtheory):
f := proc(n) local t1, v, r, x, j;
if (n = 1) then return 1; end if;
t1 := ifactors(n): v := 0;
for x in op(2, t1) do r := pi(x[1]):
for j from 1 to x[2] do
v := v * 10^length(r) + r;
end do; end do; v; end proc;


MATHEMATICA

f[n_] := If[n == 1, 1, FromDigits@ Flatten[ IntegerDigits@# & /@ (PrimePi@# & /@ Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@ n])]]; Array[f, 61] (* Robert G. Wilson v, Jun 06 2011 *)


PROG

(Haskell)
a087712 1 = 1
a087712 n = read $ concatMap (show . a049084) $ a027746_row n :: Integer
 Reinhard Zumkeller, Oct 03 2012


CROSSREFS

See A098282 for lengths of trajectories. Cf. A077960, A156055.
Cf. A027746, A049084.
Sequence in context: A121713 A357820 A134242 * A180702 A263328 A081926
Adjacent sequences: A087709 A087710 A087711 * A087713 A087714 A087715


KEYWORD

nonn,base,look


AUTHOR

Eric Angelini, Feb 02 2009


EXTENSIONS

More terms from R. J. Mathar (Feb 08 2009) and independently from David Applegate and N. J. A. Sloane, Feb 09 2009


STATUS

approved



