login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A087712 a(1) = 1; if n = k-th prime, a(n) = k; otherwise write all prime factors of n in nondecreasing order, replace each prime with its rank, and concatenate the ranks. 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Concatenations of consecutive entries of A112798. - R. J. Mathar, Feb 09 2009
The old entry with this A-number was a duplicate of A082467.
LINKS
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.
Sequence in context: A121713 A357820 A134242 * A180702 A263328 A081926
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 25 05:14 EST 2024. Contains 370310 sequences. (Running on oeis4.)