A337427 a(n) is the least prime of the form (3^r*5^s*7^t - 1)/2, r, s, t > 0, r + s + t = n.

157, 787, 3307, 19687, 12757, 347287, 267907, 3125587, 2870437, 5166787, 25833937, 590736037, 232505437, 2712563437, 13562817187, 3766588087, 52313723437, 726579492187, 332213069317, 847482319687, 4237411598437, 115351760179687, 88985643567187, 68646067894687

Offset

4,1

Links

David A. Corneth, Table of n, a(n) for n = 4..507

Example

For exponent sum n = 3 no prime exists, (3*5*7-1)/2 = 52 is composite.
a(4) = 157: (3^2*5*7-1)/2 is the least prime with exponent sum n = 4.
a(5) = 787: there are 6 ways to choose the exponents of 3, 5, 7 with sum n = 5, i.e., [3,1,1], [1,3,1], [1,1,3], [2,2,1], [2,1,2], [1,2,2]. (3^3*5*7-1)/2 = 472 is composite, but (3^2*5^2*7-1)/2 = 787 is prime.

Mathematica

Table[Min[Select[(3^#[[1]] 5^#[[2]] 7^#[[3]]-1)/2&/@Flatten[Permutations/@ IntegerPartitions[n, {3}], 1], PrimeQ]], {n, 30}]/.\[Infinity]->Nothing (* Harvey P. Dale, Oct 29 2020 *)

Prog

(PARI) seqpp(np0, np, add, lim) = {for(m=np0, lim, my(pmin=oo); forpart(V=m, forperm(np, P, my(p=(prod(k=1, np, prime(k+1)^V[P[k]])+add)/2); if(isprime(p), pmin=min(pmin, p))), [1, m-np+1], [np, np]); print1(pmin, ", "))};
seqpp(4, 3, -1, 27)

Crossrefs

Cf. A337423, A337425, A337428.

Sequence in context: A142478 A052028 A226972 * A142766 A326442 A258436

Adjacent sequences: A337424 A337425 A337426 * A337428 A337429 A337430

Keyword

nonn

Author

Hugo Pfoertner, Aug 29 2020

Status

approved