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Numbers k such that prime(k) + prime(k+1) is a perfect power.
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%I #7 Jan 09 2019 01:54:24

%S 2,7,15,18,20,28,61,152,190,293,377,492,558,564,789,919,942,1332,1768,

%T 2343,2429,2693,2952,3136,3720,3928,4837,5421,5722,6870,7347,8126,

%U 8193,9465,9857,9927,10410,10483,10653,12685,13005,13763,13955,16033,16342

%N Numbers k such that prime(k) + prime(k+1) is a perfect power.

%C First terms absent in A064397: 2, 18, 28, 564, 1332, 3928, 12415, 13005, 16886.

%e 2 is a term because prime(2) + prime(3) = 3 + 5 = 8 = 2^3 (perfect power);

%e 7 is a term because prime(7) + prime(8) = 17 + 19 = 36 = 6^2 (perfect power);

%e 39867 is a term because prime(39867) + prime(39868) = 478241 + 478243 = 956484 = 978^2 (perfect power).

%o (PARI) s=[];for(n=1,41530,a=prime(n)+prime(n+1);if(ispower(a),s=concat(s,n)));s

%Y Cf. A064397 (numbers k such that prime(k) + prime(k+1) is a square).

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 17 2007