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A340392 Primes of the form Sum_{k=i..j} k^k.

%I A340392 #11 Jan 06 2021 12:32:06
%S A340392 5,31,283,3413,50069,17650823,10405071317,449317973725128511,
%T A340392 18895749970915969007,18896062057839748031,846136323944176515589,
%U A340392 40192544390028896900861,40192544398944997349117,40192544399240696440217,208492413443704093346554910065262730566475781
%N A340392 Primes of the form Sum_{k=i..j} k^k.
%H A340392 Robert Israel, <a href="/A340392/b340392.txt">Table of n, a(n) for n = 1..90</a>
%e A340392 a(1) = 5 = 1^1 + 2^2 is prime.
%e A340392 a(2) = 31 = 2^2 + 3^3 is prime.
%e A340392 a(3) = 283 = 3^3 + 4^4 is prime.
%e A340392 a(4) = 3413 = 1^1 + 2^2 + 3^3 + 4^4 + 5^5 is prime.
%e A340392 a(5) = 50069 = 1^1 + 2^2 + 3^3 + 4^4 + 5^5 + 6^6 is prime.
%e A340392 a(6) = 17650823 = 3^3 + 4^4 + 5^5 + 6^6 + 7^7 + 8^8 is prime.
%p A340392 B:= [0,seq(i^i,i=1..100)]:
%p A340392 S:= ListTools:-PartialSums(B):
%p A340392 R:=select(t -> t < 101^101 and isprime(t), {seq(seq(S[i]-S[j],j=1..i-1),i=2..101)}):
%p A340392 sort(convert(R,list));
%Y A340392 Cf. A073826.
%K A340392 nonn
%O A340392 1,1
%A A340392 _J. M. Bergot_ and _Robert Israel_, Jan 05 2021