A276455 Primes of the form Sum_{k=1..n} k^(k-1).

3, 701, 45269999

Offset

1,1

Comments

Searched up to n = 5000.

a(4) has 38019 digits (1973212031 ... 7493445627) and corresponds to n=9553. - Robert Price, Sep 23 2016; [number of digits in a(4) corrected by Jon E. Schoenfield, Nov 06 2016]

No other primes corresponding to n < 80000. - Robert Price, Mar 17 2017

Links

Table of n, a(n) for n=1..3.

Sebastiao Antonio da Silva, Prime Curios: 9^8 + 8^7 + 7^6 + 6^5 + 5^4 + 4^3 + 3^2 + 2^1 + 1^0 is prime

Example

3 is in the sequence because 3 is prime and 3 = 2^1 + 1^0.
701 is in the sequence because 701 is prime and 701 = 5^4 + 4^3 + 3^2 + 2^1 + 1^0.
45269999 is in the sequence because 45269999 is prime and 45269999 = 9^8 + 8^7 + 7^6 + 6^5 + 5^4 + 4^3 + 3^2 + 2^1 + 1^0.

Mathematica

Select[Accumulate[Table[n^(n-1), {n, 100}]], PrimeQ] (* Harvey P. Dale, Apr 13 2020 *)

Prog

(Sage)
sum = 0
seq = []
max_n = 2500
for n in range(1, max_n+1):
    sum += n^(n-1)
    if is_prime(sum):
        seq.append(n)
print(seq)

Crossrefs

Primes in A060946.

Sequence in context: A266639 A203496 A308323 * A231604 A306961 A059120

Adjacent sequences: A276452 A276453 A276454 * A276456 A276457 A276458

Keyword

nonn,bref

Author

Robert C. Lyons, Sep 06 2016

Status

approved