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URL: https://oeis.org/A393151

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A393151
Least prime representable as a sum of n prime powers using each of the first 2n primes exactly once as bases and exponents, and -1 if no such number exists.
0
-1, -1, 18307, 112105843, 1793060726797, 10089795754966163, 5480903094928438857619, 81872643259787173972610143, 4316742844900502599568730017541461, 17761888924321463357789870295452355955736467
OFFSET
1,3
COMMENTS
If a(n) != -1, a(n) >= A392412(n).
a(3) = A392412(3) and a(9) = A392412(9).
EXAMPLE
a(3) = 7^5 + 11^3 + 13^2 = 18307 is prime.
a(4) = 2^19 + 5^11 + 13^7 + 17^3 = 112105843 is prime.
a(5) = 13^11 + 17^2 + 19^7 + 23^5 + 29^3 = 1793060726797 is prime.
a(6) = 2^31 + 3^29 + 17^13 + 19^11 + 23^5 + 37^7 = 10089795754966163 is prime.
a(7) = 19^17 + 23^13 + 29^11 + 31^3 + 37^2 + 41^5 + 43^7 = 5480903094928438857619 is prime.
a(8) = 2^41 + 23^19 + 29^17 + 31^13 + 37^11 + 43^7 + 47^5 + 53^3 = 81872643259787173972610143 is prime.
a(9) = 29^23 + 31^19 + 37^17 + 41^13 + 43^11 + 47^7 + 53^5 + 59^3 + 61^2 = 4316742844900502599568730017541461 is prime.
a(10) = 2^67 + 31^29 + 37^23 + 41^19 + 43^17 + 47^13 + 53^5 + 59^7 + 61^11 + 71^3 = 17761888924321463357789870295452355955736467 is prime.
PROG
(PARI) a(n) =my(u = primes(2*n), p2 = prime(2*n), pexp = prime(n+1), mmax = n * p2^pexp, candidats = List(), m = mmax); forsubset([2*n, n], s, my(sv = Vec(s), v = vector(n, i, u[sv[i]]), w = Vecrev(setminus(Set(u), Set(v)))); forperm(#w, p, my(pp = Vec(p), x = sum(i=1, n, v[i]^w[pp[i]])); if (x > mmax, next); if (ispseudoprime(x), listput(candidats, x); if (x < m, m = x)))); if (#candidats, return(m)); return(-1) \\ code appropriate for n <= 9.
CROSSREFS
Sequence in context: A023340 A232142 A237737 * A145822 A286035 A217049
KEYWORD
sign,more
AUTHOR
Jean-Marc Rebert, Feb 03 2026
EXTENSIONS
a(10) from Sean A. Irvine, Feb 19 2026
STATUS
approved