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%I #15 Feb 18 2022 05:17:26
%S 2203,77983,90863,185477,371087,388573,613607,912349,1293899,1600919,
%T 2146457,30661333,35608189,48823147,81190429,105823093,122753857,
%U 204341747,338602837,368601707,374788121,426958673,498675409,586371239,656232799,665360321,674509487,693132527
%N Prime averages of two successive perfect powers (A001597(k) + A001597(k+1))/2.
%e 2203 = (A001597(61)+A001597(62))/2 = (2197+2209)/2.
%t a = Select[Range[2, 50000000], GCD @@ (Transpose[FactorInteger[ # ]][[2]]) > 1 &]; sizea = Length[a]; (a[[Select[Range[sizea - 1], PrimeQ[(a[[ # ]] + a[[ # + 1]])/2] &]]] + a[[Select[Range[sizea - 1], PrimeQ[(a[[ # ]] + a[[ # + 1]])/2] &] + 1]])/2 (* _Tanya Khovanova_, Sep 15 2007 *)
%Y Cf. A001597.
%K easy,nonn
%O 1,1
%A _Zak Seidov_, Oct 11 2002
%E More terms from _Tanya Khovanova_, Sep 15 2007
%E More terms from _Amiram Eldar_, Feb 18 2022
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