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%I #8 Feb 22 2017 03:47:18
%S 3,4,5,7,9,10,14,15,16,18,21,24,26,27,28,30,35,36,39,42,43,44,45,46,
%T 47,49,50,54,55,56,58,60,66,69,72,74,76,78,80,82,83,87,88,93,98,99,
%U 103,104,105,106,108,110,111,114,115,116,118,120,122,123,126,127
%N 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.
%C The corresponding primes are 3,7,3,19,7,19,13,67,83,101,61,73,...
%H Charles R Greathouse IV, <a href="/A282808/b282808.txt">Table of n, a(n) for n = 1..10000</a>
%t 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 *)
%o (PARI) oddpart(n)=n>>valuation(n,2)
%o 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
%Y Cf. A000040, A000265.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Feb 21 2017
%E More terms from _Peter J. C. Moses_, Feb 21 2017
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