A211414 Inverse of permutation in A215261.

1, 3, 5, 10, 7, 2, 9, 11, 4, 22, 13, 15, 17, 6, 16, 19, 21, 23, 25, 27, 12, 8, 29, 31, 14, 20, 33, 35, 37, 39, 41, 43, 26, 18, 24, 45, 47, 36, 32, 49, 51, 53, 55, 57, 59, 38, 61, 63, 30, 65, 34, 67, 69, 71, 28, 73, 42, 40, 75, 77, 79, 46, 81, 83, 44, 85, 87

Offset

1,2

Comments

Permutation of the natural numbers A000027 with inverse permutation A215261.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Maple

issp:= n-> not isprime(n) and numtheory[bigomega](n)=2:
sp:= proc(n) option remember; local k; if n=1 then 4 else
       for k from 1+sp(n-1) while not issp(k) do od; k fi end:
nsp:= proc(n) option remember; local k; if n=1 then 1 else
        for k from 1+nsp(n-1) while issp(k) do od; k fi end:
g:= proc() true end:
b:= proc(n) option remember; local k, s;
      if n>1 then b(n-1) fi;
      if irem(n, 2, 'r')=1 then nsp(r+1)
    else for k do s:=sp(k); if g(s) and not issp(nsp(r)+s) and
           not issp(nsp(r+1)+s) then g(s):= false; return s fi od
      fi
    end:
a:= proc() local t, a; t, a:= 0, proc() -1 end;
      proc(n) local h;
        while a(n) = -1 do
          t:= t+1; h:= b(t);
          if a(h) = -1 then a(h):= t fi
        od; a(n)
      end
    end():
seq(a(n), n=1..100);

Mathematica

issp[n_] := ! PrimeQ[n] && PrimeOmega[n] == 2;
sp[n_] := sp[n] = If[n == 1, 4, For[k = 1+sp[n-1], !issp[k], k++]; k];
nsp[n_] := nsp[n] = If[n == 1, 1, For[k = 1+nsp[n-1], issp[k], k++]; k];
Clear[g]; g[_] = True;
b[n_] := b[n] = Module[{q, r, k, s}, If[n > 1, b[n-1]]; {q, r} = QuotientRemainder[n, 2]; If[r == 1, nsp[q+1], For[k = 1, True, k++, s = sp[k]; If[g[s] && !issp[nsp[q]+s] && !issp[nsp[q+1]+s], g[s] = False; Return[s]]]]];
a[n_] := For[k = 1, True, k++, If[b[k] == n, Return[k]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Aug 30 2021, after Maple code *)

Crossrefs

Cf. A000027, A215261.

Sequence in context: A188983 A083519 A302088 * A173706 A365440 A332359

Adjacent sequences: A211411 A211412 A211413 * A211415 A211416 A211417

Keyword

nonn,easy

Author

Jonathan Vos Post and Alois P. Heinz, Feb 18 2013

Status

approved