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 A085106 Starting with composite(n) go on adding smaller composite numbers until one gets a prime. a(n) = this prime, or 0 if no such prime exists. 1
 0, 0, 0, 17, 19, 31, 53, 29, 31, 0, 83, 41, 43, 67, 71, 97, 53, 173, 223, 349, 337, 67, 337, 71, 109, 113, 79, 359, 239, 89, 0, 139, 97, 193, 101, 103, 157, 109, 367, 113, 383, 443, 293, 761, 127, 1021, 131, 199, 137, 139, 211, 353, 149, 151, 647, 659, 311, 239, 163 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Conjecture: No entry is zero for n >10. There are only four terms which are zero. The conjecture is false as a(31) is zero.  There is, however, no further zero up to a(26754), so the conjecture may be rephrased as: no entry is zero for n>31 and there are only five terms which are zero. - Harvey P. Dale, May 04 2015 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE Composite(6) = 12 and 12+10+9 = 31 hence a(6) = 31. MATHEMATICA With[{c=Reverse[Select[Range[100], CompositeQ]]}, SelectFirst[#, PrimeQ]&/@Table[Accumulate[Take[c, -n]], {n, Length[c]}]]/.{Missing["NotFound"] -> 0} (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, May 04 2015 *) PROG (PARI) for (n = 4, 120, if (!isprime(n), s = n; k = n - 1; while (!isprime(s) && k > 3, if (!isprime(k), s += k); k--); print1(if (isprime(s), s, 0), " "))); (Wasserman) CROSSREFS Cf. A085105. Sequence in context: A290634 A182570 A292237 * A079592 A160027 A288407 Adjacent sequences:  A085103 A085104 A085105 * A085107 A085108 A085109 KEYWORD nonn AUTHOR Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 04 2003 EXTENSIONS More terms from David Wasserman, Jan 27 2005 STATUS approved

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Last modified April 15 07:59 EDT 2021. Contains 342975 sequences. (Running on oeis4.)