A178379 Semiprimes of the form m*k such that (m+1)/(k-1) is prime.

4, 9, 15, 35, 39, 55, 77, 95, 111, 119, 183, 203, 209, 215, 219, 287, 299, 319, 335, 471, 527, 579, 707, 767, 791, 799, 815, 831, 939, 959, 989, 1007, 1055, 1079, 1191, 1199, 1211, 1263, 1343, 1371, 1415, 1623, 1655, 1691, 1703, 1799, 1829, 1839, 1967, 1983

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1) = 4 because 4 = 2*2 and (2+1)/(2-1) = 3 is prime,
a(2) = 9 because 9 = 3*3 and (3+1)/(3-1) = 2 is prime,
a(3) = 15 because 15 = 5*3 and (5+1)/(3-1) = 3 is prime,
a(4) = 35 because 35 = 7*5 and (7+1)/(5-1) = 2 is prime,
a(5) = 39 because 39 = 13*3 and (13+1)/(3-1) = 7 is prime.

Maple

N:= 2000: # to get all terms <= N
P:= select(isprime, [2, seq(i, i=3..N/3, 2)]):
Res:= NULL:
for p in P do  qmax:= min(p, N/p);
  for q in P do
    if q > qmax then break fi;
    v:= (p+1)/(q-1);
    if v::integer and isprime(v) then Res:= Res, q*p fiod od:
sort([Res]); # Robert Israel, Jul 28 2020

Crossrefs

Cf. A000040, A001358.

Sequence in context: A122964 A301254 A291318 * A228553 A356928 A357807

Adjacent sequences: A178376 A178377 A178378 * A178380 A178381 A178382

Keyword

nonn

Author

Juri-Stepan Gerasimov, May 26 2010

Extensions

More terms from R. J. Mathar, May 28 2010

Status

approved