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%I #15 Sep 13 2019 08:04:52
%S 5,7,199,283,349,463,643,823,859,1291,1699,1723,1789,1879,2083,2143,
%T 2383,2551,2803,3259,3541,3559,3931,4021,4243,4639,4723,5443,5479,
%U 5503,5659,6451,6691,6703,6763,6829,6949,7459,7591,7879,8011,8389,8539,8599,8629
%N Greater of twin primes p, p+2 with unique values of sigma(p) and sigma(p+2); sigma(n) = A000203(n) = sum of divisors of n.
%C Subsequence of A211656, A211660, and A211678.
%H Amiram Eldar, <a href="/A211769/b211769.txt">Table of n, a(n) for n = 1..10000</a>
%e Prime 199 is in sequence because 197 and 199 are twin primes, sigma(197) = 198, sigma(199) = 200 and there are no other numbers m, n with sigma(m) = 198 or sigma(n) = 200.
%t d = DivisorSigma[1, Range[10000]]; t = Transpose[Select[Tally[Sort[d]], #[[2]] == 1 && #[[1]] <= Length[d] &]][[1]]; t2 = Sort[Flatten[Table[Position[d, i], {i, t}]]]; t3 = Select[t2, PrimeQ]; tp = {}; Do[If[t3[[i + 1]] - t3[[i]] == 2, AppendTo[tp, t3[[i + 1]]]], {i, Length[t3] - 1}]; tp (* _T. D. Noe_, Apr 26 2012 *)
%Y Cf. A211678 (twin primes p, p+2 with unique values of sigma(p) and sigma(p+2)), A211767 (lesser of twin primes p, p+2 with unique values of sigma(p) and sigma(p+2)).
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Apr 20 2012
%E A-number corrected by _Jaroslav Krizek_, Mar 17 2013
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