A392412 Smallest sum of n powers, where all bases and exponents are different primes.

8, 174, 18307, 19863738, 1792573221817, 10021071717171912, 5480903094684086387989, 81872643259784897802638556, 4316742844900502599568730017541461, 17761888924321463357789688476618084642025176, 4172880980943649737519154399519049993250057256249

Offset

1,1

Comments

For the data given, except a(1), the largest component to be summed to make the term a(n) is prime(n+1)^prime(n), where prime(n) is the n-th prime.

Links

Table of n, a(n) for n=1..11.

Formula

a(n) = prime(2*n)^prime(1) + ... + prime(n+1)^prime(n) for n >= 2. - Pontus von Brömssen, Jan 23 2026

Example

a(2) = 7^2 + 5^3 = 49 + 125 = 174.
a(5) = 29^2 + 23^3 + 19^5 + 17^7 + 13^11 = 1792573221817.

Crossrefs

Cf. A053810.

Sequence in context: A138783 A067637 A357503 * A024109 A027464 A220966

Adjacent sequences: A392409 A392410 A392411 * A392413 A392414 A392415

Keyword

nonn,easy

Author

Paul Duckett, Jan 10 2026

Status

approved