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%I #45 Aug 30 2021 12:53:28
%S 1,6,2,9,3,14,5,22,7,4,8,21,11,25,12,15,13,34,16,26,17,10,18,35,19,33,
%T 20,55,23,49,24,39,27,51,28,38,29,46,30,58,31,57,32,65,36,62,37,77,40,
%U 69,41,85,42,74,43,82,44,86,45,91,47,106,48,87,50,115,52
%N Write down the nonsemiprime numbers 1, 2, 3, 5, 7, 8, 11, 12, 13, 16, 17, ... and insert between two nonsemiprimes the smallest semiprime not yet present in the sequence such that two neighboring integers sum to a nonsemiprime.
%C This is to semiprimes A001358 as A222307 is to primes A000040.
%C This is a permutation of the natural numbers A000027 with inverse permutation A211414.
%H Alois P. Heinz, <a href="/A215261/b215261.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%p issp:= n-> not isprime(n) and numtheory[bigomega](n)=2:
%p sp:= proc(n) option remember; local k; if n=1 then 4 else
%p for k from 1+sp(n-1) while not issp(k) do od; k fi end:
%p nsp:= proc(n) option remember; local k; if n=1 then 1 else
%p for k from 1+nsp(n-1) while issp(k) do od; k fi end:
%p g:= proc() true end:
%p a:= proc(n) option remember; local k, s;
%p if n>1 then a(n-1) fi;
%p if irem(n, 2, 'r')=1 then nsp(r+1)
%p else for k do s:=sp(k); if g(s) and not issp(nsp(r)+s) and
%p not issp(nsp(r+1)+s) then g(s):= false; return s fi od
%p fi
%p end:
%p seq(a(n), n=1..80);
%t issp[n_] := !PrimeQ[n] && PrimeOmega[n] == 2;
%t sp[n_] := sp[n] = If[n == 1, 4, For[k = 1 + sp[n-1], !issp[k], k++]; k];
%t nsp[n_] := nsp[n] = If[n == 1, 1, For[k = 1 + nsp[n-1], issp[k], k++]; k];
%t Clear[g]; g[_] = True;
%t a[n_] := a[n] = Module[{q, r, k, s}, If[n>1, a[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]]]]];
%t Table[a[n], {n, 1, 80}] (* _Jean-François Alcover_, Mar 24 2017, translated from Maple *)
%Y Cf. A001358, A211414, A222307.
%K nonn,easy
%O 1,2
%A _Jonathan Vos Post_ and _Alois P. Heinz_, Feb 17 2013
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