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 A085042 Smallest multiple of the n-th prime such that every partial sum is a prime, or 0 if no such number exists. 2
 2, 3, 0, 14, 22, 26, 34, 38, 138, 232, 62, 148, 164, 516, 94, 318, 1298, 610, 134, 568, 146, 2212, 1494, 356, 1552, 1212, 618, 642, 2616, 1808, 762, 3144, 1096, 1668, 1490, 604, 942, 326, 1002, 2076, 2506, 1448, 2292, 1158, 7092, 4776, 2532, 892, 908, 2290 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(3) = 0, as 2+3 = 5 and 5 + k*5 cannot be a prime unless k = 0. Every term after the third is obviously even. From Robert Israel, Dec 25 2016: (Start) a(n) = 0 if and only if Sum_{j 1 then     A:= A, 0;   else     for j from 1 do if isprime(s+j*p) then       A:= A, j*p;       s:= s+j*p;       break     fi od;   fi od: A; # Robert Israel, Dec 25 2016 MATHEMATICA f[s_List] := Block[{k = 2, p = Prime[1 + Length@ s], t = Plus @@ s}, While[ !PrimeQ[k*p + t], k += 2]; Append[s, p*k]]; Nest[f, {2, 3, 0}, 50] (* Robert G. Wilson v, Dec 25 2016 *) CROSSREFS Cf. A085043. Sequence in context: A219341 A059740 A005160 * A096542 A009206 A318146 Adjacent sequences:  A085039 A085040 A085041 * A085043 A085044 A085045 KEYWORD nonn AUTHOR Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 19 2003 EXTENSIONS More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jun 25 2003 STATUS approved

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Last modified April 7 14:55 EDT 2020. Contains 333305 sequences. (Running on oeis4.)