A087712 - OEIS

%I #35 Oct 01 2024 13:17:05

%S 1,1,2,11,3,12,4,111,22,13,5,112,6,14,23,1111,7,122,8,113,24,15,9,

%T 1112,33,16,222,114,10,123,11,11111,25,17,34,1122,12,18,26,1113,13,

%U 124,14,115,223,19,15,11112,44,133,27,116,16,1222,35,1114,28,110,17,1123,18

%N 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.

%C Concatenations of consecutive entries of A112798. - _R. J. Mathar_, Feb 09 2009

%C The old entry with this A-number was a duplicate of A082467.

%H Reinhard Zumkeller, <a href="/A087712/b087712.txt">Table of n, a(n) for n = 1..10000</a>

%e n = 2 = first prime, a(2) = 1.

%e n = 3 = second prime, a(3) = 2.

%e n = 4 = 2*2 -> 1,1 -> 11, so a(4) = 11.

%e n = 6 = 2*3 -> 1,2 -> 12, so a(6) = 12.

%e n = 12 = 2*2*3 -> 1,1,2 -> 112, so a(12) = 112.

%p # Maple program from _R. J. Mathar_, Feb 08 2009: (Start)

%p cat2 := proc(a,b) a*10^(max(1,ilog10(b)+1))+b ; end:

%p A049084 := proc(p) if isprime(p) then numtheory[pi](p) ; else 0 ; fi; end:

%p 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:

%p seq(A087712(n),n=1..140); # (End)

%p # (Maple program from _David Applegate_ and _N. J. A. Sloane_, Feb 09 2009)

%p with(numtheory):

%p f := proc(n) local t1, v, r, x, j;

%p if (n = 1) then return 1; end if;

%p t1 := ifactors(n): v := 0;

%p for x in op(2,t1) do r := pi(x[1]):

%p for j from 1 to x[2] do

%p v := v * 10^length(r) + r;

%p end do; end do; v; end proc;

%t 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 *)

%o (Haskell)

%o a087712 1 = 1

%o a087712 n = read $ concatMap (show . a049084) $ a027746_row n :: Integer

%o -- _Reinhard Zumkeller_, Oct 03 2012

%o (Python)

%o from sympy import factorint, primepi

%o def a(n):

%o     if n == 1: return 1

%o     return int("".join(str(primepi(p))*e for p, e in factorint(n).items()))

%o print([a(n) for n in range(1, 62)]) # _Michael S. Branicky_, Oct 01 2024

%Y See A098282 for lengths of trajectories. Cf. A077960, A156055.

%Y Cf. A027746, A049084.

%K nonn,base,look

%O 1,3

%A _Eric Angelini_, Feb 02 2009

%E More terms from _R. J. Mathar_ (Feb 08 2009) and independently from _David Applegate_ and _N. J. A. Sloane_, Feb 09 2009