A234101 Primes of the form (p*q*r - 1)/2, where p, q, r are distinct primes.

97, 127, 199, 227, 241, 277, 307, 313, 331, 379, 397, 457, 467, 547, 617, 619, 647, 709, 727, 739, 757, 773, 797, 829, 883, 977, 1033, 1069, 1117, 1123, 1171, 1193, 1277, 1297, 1303, 1319, 1423, 1447, 1459, 1483, 1609, 1621, 1667, 1697, 1699, 1747, 1753

Offset

1,1

Links

Chris R. Rehmann, Table of n, a(n) for n = 1..10000

Example

(See A234100.)

Mathematica

t = Select[Range[1, 10000, 2], Map[Last, FactorInteger[#]] == Table[1, {3}] &]; Take[(t - 1)/2, 120] (* A234099 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A234100 *)
(w - 1)/2 (* A234101 *)    (* Peter J. C. Moses, Dec 23 2013 *)

Prog

(MATLAB)
a = []; N = 1753; p = primes(N);
for k = 1:length(p)
    f = factor(2*p(k)+1); u = unique(f);
    if isequal(f, u) && length(u)==3
        a(end+1) = p(k);
    end
end
disp(regexprep(num2str(a), ' +', ', ')) % Chris R. Rehmann, May 24 2026

Crossrefs

Cf. A234099, A234100, A234093, A234102.

Sequence in context: A140830 A038133 A144325 * A161367 A216311 A258877

Adjacent sequences: A234098 A234099 A234100 * A234102 A234103 A234104

Keyword

nonn,easy

Author

Clark Kimberling, Dec 27 2013

Status

approved