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 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 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

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