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 A282808 a(1)=3; for n>=2, a(n) is  the smallest m>a(n-1) such that odd part of a(1) + ... + a(n-1) + m is prime. 1
 3, 4, 5, 7, 9, 10, 14, 15, 16, 18, 21, 24, 26, 27, 28, 30, 35, 36, 39, 42, 43, 44, 45, 46, 47, 49, 50, 54, 55, 56, 58, 60, 66, 69, 72, 74, 76, 78, 80, 82, 83, 87, 88, 93, 98, 99, 103, 104, 105, 106, 108, 110, 111, 114, 115, 116, 118, 120, 122, 123, 126, 127 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding primes are 3,7,3,19,7,19,13,67,83,101,61,73,... LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 MATHEMATICA a[1]=3; s[1]=3; s[n_] := s[n-1]+a[n]; a[n_]:=a[n]=Block[{m, u}, For[m = a[n-1] + 1, u = s[n-1] + m; ! PrimeQ[ u/ 2^IntegerExponent[u, 2]], m++]; m]; Array[a, 62] (* Giovanni Resta, Feb 21 2017 *) PROG (PARI) oddpart(n)=n>>valuation(n, 2) first(n)=my(v=vector(n), s, m); v[1]=s=3; for(k=2, n, m=v[k-1]; while(!isprime(oddpart(m+++s)), ); s+=m; v[k]=m); v \\ Charles R Greathouse IV, Feb 22 2017 CROSSREFS Cf. A000040, A000265. Sequence in context: A136014 A112930 A224985 * A260401 A003159 A187691 Adjacent sequences:  A282805 A282806 A282807 * A282809 A282810 A282811 KEYWORD nonn AUTHOR Vladimir Shevelev, Feb 21 2017 EXTENSIONS More terms from Peter J. C. Moses, Feb 21 2017 STATUS approved

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Last modified April 5 13:02 EDT 2020. Contains 333241 sequences. (Running on oeis4.)