cp's OEIS Frontend

A132746 Numbers k such that prime(k) + prime(k+1) is a perfect power.

%I A132746 #16 Mar 08 2025 18:38:32
%S A132746 2,7,15,18,20,28,61,152,190,293,377,492,558,564,789,919,942,1332,1768,
%T A132746 2343,2429,2693,2952,3136,3720,3928,4837,5421,5722,6870,7347,8126,
%U A132746 8193,9465,9857,9927,10410,10483,10653,12685,13005,13763,13955,16033,16342
%N A132746 Numbers k such that prime(k) + prime(k+1) is a perfect power.
%C A132746 First terms absent in A064397: 2, 18, 28, 564, 1332, 3928, 12415, 13005, 16886.
%F A132746 a(n) >> n^2/log^2 n. - _Charles R Greathouse IV_, Mar 08 2025
%e A132746 2 is a term because prime(2) + prime(3) = 3 + 5 = 8 = 2^3 (perfect power);
%e A132746 7 is a term because prime(7) + prime(8) = 17 + 19 = 36 = 6^2 (perfect power);
%e A132746 39867 is a term because prime(39867) + prime(39868) = 478241 + 478243 = 956484 = 978^2 (perfect power).
%t A132746 Select[Range[16342],ResourceFunction["PerfectPowerQ"][Prime[#]+Prime[#+1]]&] (* _James C. McMahon_, Mar 08 2025 *)
%o A132746 (PARI) s=[];for(n=1,41530,a=prime(n)+prime(n+1);if(ispower(a),s=concat(s,n)));s
%Y A132746 Cf. A064397 (numbers k such that prime(k) + prime(k+1) is a square).
%Y A132746 Cf. A001043, A001597.
%K A132746 nonn
%O A132746 1,1
%A A132746 _Zak Seidov_, Nov 17 2007