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A208662 Smallest m such that the n-th odd prime is the smallest prime for all decompositions of 2*m into two primes.

%I A208662 #15 Feb 16 2025 08:33:16
%S A208662 3,6,15,62,61,209,49,110,173,154,637,572,481,278,1256,1763,691,928,
%T A208662 2309,496,1909,3716,6389,2989,13049,1321,11633,5134,9848,3004,17096,
%U A208662 11303,2686,18884,6781,4798,11416,29957,3713,44393,25156,48884,24001,56279,30031
%N A208662 Smallest m such that the n-th odd prime is the smallest prime for all decompositions of 2*m into two primes.
%C A208662 A002373(a(n)) = A065091(n) and A002373(m) != A065091(n) for m < a(n).
%H A208662 Reinhard Zumkeller, <a href="/A208662/b208662.txt">Table of n, a(n) for n = 1..120</a>
%H A208662 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A208662 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A208662 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e A208662 n=3, a(3)=15: 7 is the 3rd odd prime and the smallest prime in all Goldbach decompositions of 2*15 = 30 = {7+23, 11+19, 13+17}, and 7 doesn't occur as smallest prime in all Goldbach decompositions for even numbers less than 30.
%o A208662 (Haskell)
%o A208662 a208662 n = head [m | m <- [1..], let p = a065091 n,
%o A208662    let q = 2 * m - p, a010051' q == 1,
%o A208662    all ((== 0) . a010051') $ map (2 * m -) $ take (n - 1) a065091_list]
%o A208662 -- _Reinhard Zumkeller_, Aug 11 2015, Feb 29 2012
%Y A208662 Cf. A002373, A065091, A260485.
%K A208662 nonn
%O A208662 1,1
%A A208662 _Reinhard Zumkeller_, Feb 29 2012