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%I #34 Feb 24 2020 14:25:50
%S 7,194,219
%N Numbers k such that Sum_{j=1..k} composite(j)^composite(j) is prime, where composite(j) is the j-th composite number.
%C If it exists, a(4) > 25800.
%e 7 is a term because for the first 7 composites, 4^4 + 6^6 + 8^8 + 9^9 + 10^10 + 12^12 + 14^14 = 11120933330250889 is prime.
%t f[ n_Integer ] := Block[ {k = n + PrimePi[ n ] + 1}, While[ k - PrimePi[ k ] - 1 != n, k++ ]; k ]; s = 0; Do[ s = s + f[n]^f[n]; If[ PrimeQ[ s ], Print[ n ] ], {n, 1, 1000} ]
%Y Cf. A000040, A002808, A053782, A073826, A132637.
%K nonn,more,bref
%O 1,1
%A _Metin Sariyar_, Aug 23 2019
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