Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Oct 29 2020 18:30:23
%S 157,787,3307,19687,12757,347287,267907,3125587,2870437,5166787,
%T 25833937,590736037,232505437,2712563437,13562817187,3766588087,
%U 52313723437,726579492187,332213069317,847482319687,4237411598437,115351760179687,88985643567187,68646067894687
%N 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.
%H David A. Corneth, <a href="/A337427/b337427.txt">Table of n, a(n) for n = 4..507</a>
%e For exponent sum n = 3 no prime exists, (3*5*7-1)/2 = 52 is composite.
%e a(4) = 157: (3^2*5*7-1)/2 is the least prime with exponent sum n = 4.
%e 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.
%t 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 *)
%o (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,", "))};
%o seqpp(4,3,-1,27)
%Y Cf. A337423, A337425, A337428.
%K nonn
%O 4,1
%A _Hugo Pfoertner_, Aug 29 2020