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A330978 a(n) = (p1 + p2)/36 such that p1 >= 5 and p2 = p1 + 2 are twin primes and p1 + p2 is a k-th power with k > 1.

%I A330978 #12 May 21 2021 04:15:39
%S A330978 1,4,6,49,64,144,196,225,841,1156,1936,2601,3844,4624,5776,6241,7776,
%T A330978 8281,9801,10000,11449,15625,20164,21609,24336,26244,26569,29929,
%U A330978 36100,40804,44944,53361,60025,63504,64009,69696,87025,93636,100489,108900,109561,126025
%N A330978 a(n) = (p1 + p2)/36 such that p1 >= 5 and p2 = p1 + 2 are twin primes and p1 + p2 is a k-th power with k > 1.
%H A330978 Amiram Eldar, <a href="/A330978/b330978.txt">Table of n, a(n) for n = 1..10000</a>
%e A330978 a(1) = 1: p1 = 17 and p2 = 19 are the first such pair, with p1 + p2 = 36 = 6^2, (17 + 19)/36 = 1;
%e A330978 a(2) = 4: p1 = 71, p2 = 73; p1 + p2 = 144 = 12^2, (71 + 73)/36 = 4.
%p A330978 isa := n -> isprime(n) and isprime(n+2) and iperfpow(2*n+2) <> FAIL:
%p A330978 select(isa, [$4..1000000]): map(n -> (n+1)/18, %); # _Peter Luschny_, Jan 05 2020
%o A330978 (PARI)  my(pp=5); forprime(p=7,130000, if(p-pp==2, if(ispower(p+pp), print1((p+pp)/36,", "))); pp=p)
%Y A330978 Cf. A119768, A270231, A330980.
%K A330978 nonn
%O A330978 1,2
%A A330978 _Hugo Pfoertner_, Jan 05 2020