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 A186336 Number of ways of representing n as the sum of one or more consecutive semiprimes. 2
 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 0, 0, 0, 2, 1, 1, 1, 0, 1, 3, 0, 0, 0, 2, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 0, 1, 3, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 3, 0, 0, 1, 2, 1, 1, 0, 2, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 1, 0, 0, 0, 3, 2, 0, 1, 0, 1, 2, 0, 0, 2, 1, 0, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 EXAMPLE a(4) = 1: 4 = A001358(1) is the first semiprime. a(10) = 2: 10 = A001358(1)+A001358(2) = 4+6 = A001358(4) = 10. a(39) = 3: 39 = 6+9+10+14 = 10+14+15 = 39. MAPLE b:= proc(n) option remember; local k; if n=0 then 0 else for k from b(n-1)+1 while isprime(k) or 2<>add(i[2], i=ifactors(k)[2]) do od; k fi end: pis:= proc(n) option remember; local k; if n<4 then 0 elif n=4 then 1 else k:= pis(n-1); k +`if`(b(k+1)=n, 1 , 0) fi end: ssp:= proc(i, j) option remember; b(j) + `if`(i=j, 0, ssp(i, j-1)) end: a:= proc(n) option remember; local i, j, cnt, s; cnt:= 0; j:= pis(n); i:= j; while i>0 do s:= ssp(i, j); if sn then j:= j-1 else cnt:= cnt+1; i, j:= i-1, j-1 fi od; cnt end: seq(a(n), n=0..200); MATHEMATICA nmax = 120; sp = Select[Range[nmax], PrimeOmega[#] == 2&]; lsp = Length[sp]; Clear[a]; a[_] = 0; Do[n = Total[sp[[i ;; j]]]; a[n] = a[n]+1, {i, 1, lsp}, {j, i, lsp}]; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Mar 13 2019 *) PROG (Haskell) a186336 n = f \$ takeWhile (<= n) a001358_list where f [] = 0 f (sp:sps) = g sp sps + f sps g spSum [] = fromEnum (spSum == n) g spSum (sp:sps) | spSum < n = g (sp + spSum) sps | spSum == n = 1 | otherwise = 0 -- Reinhard Zumkeller, Feb 28 2011 CROSSREFS Cf. A001358, A112020, A186337. Sequence in context: A332712 A079126 A339086 * A025891 A341000 A120630 Adjacent sequences: A186333 A186334 A186335 * A186337 A186338 A186339 KEYWORD nonn AUTHOR Alois P. Heinz, Feb 18 2011 STATUS approved

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Last modified August 5 23:35 EDT 2024. Contains 374957 sequences. (Running on oeis4.)