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A087712
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a(1) = 1; if n = k-th prime, a(n) = k; otherwise write all prime factors of n in nondecreasing order, replace each prime by its rank, and concatenate the ranks.
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12
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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; internal format)
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OFFSET
| 1,3
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COMMENTS
| Concatenations of consecutive entries of A112798. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 09 2009]
The old entry with this A-number was a duplicate of A082467.
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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.
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MAPLE
| Maple program from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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 (njas(AT)research.att.com), 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;
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) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 09 2009]
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MATHEMATICA
| f[n_] := If[n == 1, 1, FromDigits@ Flatten[ IntegerDigits@# & /@ (PrimePi@# & /@ Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@ n])]]; Array[f, 61] (* Robert G. Wilson v, June 6 2011 *)
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CROSSREFS
| See A098282 for lengths of trajectories. Cf. A077960, A156055.
Sequence in context: A104662 A121713 A134242 * A180702 A081926 A069800
Adjacent sequences: A087709 A087710 A087711 * A087713 A087714 A087715
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KEYWORD
| nonn,base
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AUTHOR
| Eric Angelini (Eric.Angelini(AT)kntv.be), Feb 02 2009
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EXTENSIONS
| More terms from R. J. Mathar (Feb 08 2009) and independently from David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Feb 09 2009
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