A211169 The least n-almost Sophie Germain prime.

2, 4, 52, 40, 688, 4900, 63112, 178240, 38272, 5357056, 1997824, 247221760, 586504192, 707436544, 15582115840, 47145459712, 77620412416, 1871289057280, 17787921498112, 10891875057664, 146305150615552, 535618317844480, 15921951753109504, 39754688251297792

Offset

1,1

Links

Table of n, a(n) for n=1..24.

Example

a(1)=2 because 2 and 5 are primes (A000040),
a(2)=4 because 4 and 9 are semiprimes (A001358),
a(3)=52 because the pair, 52 and 105, are 3-almost primes (A014612) and they are the least such pair,
a(4)=40 because the pair, 40 and 81, are 4-almost primes (A014613) and they are the least such pair, etc.

Maple

with(numtheory);
A211169:=proc(q)
local a, b, c, d, g, f, i, j, n;
for j from 1 to q do for n from 1 to q do
    a:=ifactors(n)[2]; b:=nops(a); c:=ifactors(2*n+1)[2]; d:=nops(c); g:=0; f:=0;
    for i from 1 to b do g:=g+a[i][2]; od; for i from 1 to d do f:=f+c[i][2]; od;
    if g=f and g=j then print(n); break;
fi; od; od; end:
A211169(1000000000000);

Mathematica

t = Table[0, {20}]; k = 2; While[k < 2700000001, x = PrimeOmega[k]; If[ t[[x]] == 0 && PrimeOmega[ 2k + 1] == x, t[[x]] = k; Print[{x, k}]]; k++]; t

Crossrefs

Cf. A005384 (Sophie Germain primes), A111153 (Sophie Germain semiprimes), A111173 (Sophie Germain 3-almost primes), A111176 (Sophie Germain 4-almost primes), A211162 (Sophie Germain 5-almost primes).

Sequence in context: A303443 A277034 A156498 * A085325 A082661 A205616

Adjacent sequences: A211166 A211167 A211168 * A211170 A211171 A211172

Keyword

nonn

Author

Don Reble, Paolo P. Lava, and Robert G. Wilson v, Jan 31 2013

Extensions

a(15)-a(24) from Giovanni Resta, Jan 31 2013

Status

approved