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A215261
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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.
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2
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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, 20, 55, 23, 49, 24, 39, 27, 51, 28, 38, 29, 46, 30, 58, 31, 57, 32, 65, 36, 62, 37, 77, 40, 69, 41, 85, 42, 74, 43, 82, 44, 86, 45, 91, 47, 106, 48, 87, 50, 115, 52
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OFFSET
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1,2
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COMMENTS
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This is a permutation of the natural numbers A000027 with inverse permutation A211414.
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LINKS
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MAPLE
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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:
a:= proc(n) option remember; local k, s;
if n>1 then a(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:
seq(a(n), n=1..80);
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MATHEMATICA
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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;
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]]]]];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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