A234500 Integers of the form (p*q*r*s + 1)/2, where p, q, r, s are distinct primes.

578, 683, 893, 998, 1073, 1208, 1403, 1502, 1523, 1568, 1628, 1658, 1853, 1898, 1943, 1964, 2153, 2195, 2243, 2258, 2321, 2393, 2423, 2468, 2503, 2558, 2594, 2657, 2783, 2828, 2933, 3023, 3053, 3098, 3140, 3203, 3273, 3278, 3350, 3383, 3392, 3518, 3548, 3581

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Formula

1 + A234105.

Example

578 = (3*5*7*11 + 1)/2.

Mathematica

t = Select[Range[1, 20000, 2], Map[Last, FactorInteger[#]] == Table[1, {4}] &]; Take[(t + 1)/2, 120] (* A234500*)
v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A234501 *)
(w + 1)/2 (* A234502 *)   (* Peter J. C. Moses, Dec 23 2013 *)
With[{nn=20}, Select[Union[(Times@@#+1)/2&/@Subsets[Prime[Range[2, nn]], {4}]], #<=(105Prime[nn]+1)/2&]] (* Harvey P. Dale, Oct 18 2021 *)

Crossrefs

Cf. A234099, A234103, A234104.

Sequence in context: A252377 A252376 A031522 * A252384 A252385 A158369

Adjacent sequences: A234497 A234498 A234499 * A234501 A234502 A234503

Keyword

nonn,easy

Author

Clark Kimberling, Jan 01 2014

Status

approved