A352137 a(n) is the first start of a sequence of exactly n members of A175648 under the map k -> 3*k+4.

21, 6, 155, 1111, 77635, 25877, 16392913, 78494323

Offset

1,1

Comments

a(n), 3*a(n)+4, 3*(3*a(n)+4)+4, ..., 3^(n-1)*a(n)+2*3^(n-1)-2 are in A175648 but 3^n*a(n)+2*3^n-2 is not.

Links

Table of n, a(n) for n=1..8.

Example

a(3) = 155 because 155, 3*155+4 = 469 and 3*469+4 = 1411 are in A175648 but 3*1411+4 = 4237 is not (155 = 5*31, 159 = 3*53, 469 = 7*67, 473 - 11*43, 1411 = 17*83, and 1415 = 5*283 are semiprimes, but 4241 is prime).

Maple

f:= proc(n) option remember;
   if numtheory:-bigomega(n)=2 and numtheory:-bigomega(n+4)=2 then 1 + procname(3*n+4) else 0 fi
end proc:
V:= Vector(7): count:= 0:
for nn from 1 while count < 7 do
   v:= f(nn);
   if v > 0 and V[v] = 0 then count:= count+1; V[v]:= nn; fi
od:
convert(V, list);

Crossrefs

Cf. A001358, A175648, A352132.

Sequence in context: A358268 A351321 A040426 * A371094 A040425 A337422

Adjacent sequences: A352134 A352135 A352136 * A352138 A352139 A352140

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Mar 05 2022

Status

approved