A258195 - OEIS

A258195

Define a<+>b = odd part(odd part(a) + odd part(b)), where odd part(n) = A000265(n); a(n) is not already appeared prime of the form <+>_{1<=i<=k}i with the smallest k, or a(n)=0 if there is no such k (see comment).

%I #17 Jul 07 2015 08:01:07

%S 3,5,7,17,19,23,11,13,53,37,47,43,29,61,31,41,83,79,73,103,137,109,

%T 113,151,149,139,193,157,167,71,199,229,179,181,223,191,107,173,97,

%U 269,241,101,59,233,197,227,251,263,89,211,239,131,293,67,307,379,277

%N Define a<+>b = odd part(odd part(a) + odd part(b)), where odd part(n) = A000265(n); a(n) is not already appeared prime of the form <+>_{1<=i<=k}i with the smallest k, or a(n)=0 if there is no such k (see comment).

%C f(n)=<+>{1<=i<=n}i is defined by the following: f(1)=1, for n>=2, f(n)=f(n-1)<+>n.

%C Conjecture: the sequence is a permutation of the odd primes.

%H Peter J. C. Moses, <a href="/A258195/b258195.txt">Table of n, a(n) for n = 1..1000</a>

%t vSum[a_,b_]:=#[#[a]+#[b]]&[#/2^IntegerExponent[#,2]&];

%t DeleteDuplicates[Select[FoldList[vSum,0,Range[500]],PrimeQ]] (* _Peter J. C. Moses_, May 23 2015 *)

%Y Cf. A258193.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, May 23 2015

%E More terms from _Peter J. C. Moses_, May 23 2015