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

5, 31, 283, 3413, 50069, 17650823, 10405071317, 449317973725128511, 18895749970915969007, 18896062057839748031, 846136323944176515589, 40192544390028896900861, 40192544398944997349117, 40192544399240696440217, 208492413443704093346554910065262730566475781

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 05 2021

Keywords

• nonn

Examples

			a(1) = 5 = 1^1 + 2^2 is prime.
a(2) = 31 = 2^2 + 3^3 is prime.
a(3) = 283 = 3^3 + 4^4 is prime.
a(4) = 3413 = 1^1 + 2^2 + 3^3 + 4^4 + 5^5 is prime.
a(5) = 50069 = 1^1 + 2^2 + 3^3 + 4^4 + 5^5 + 6^6 is prime.
a(6) = 17650823 = 3^3 + 4^4 + 5^5 + 6^6 + 7^7 + 8^8 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..90

Crossrefs

Cf. A073826.

Programs

Maple

B:= [0,seq(i^i,i=1..100)]:
S:= ListTools:-PartialSums(B):
R:=select(t -> t < 101^101 and isprime(t), {seq(seq(S[i]-S[j],j=1..i-1),i=2..101)}):
sort(convert(R,list));