

A211169


The least nalmost Sophie Germain prime.


1



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

1,1


LINKS



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 3almost primes (A014612) and they are the least such pair,
a(4)=40 because the pair, 40 and 81, are 4almost primes (A014613) and they are the least such pair, etc.


MAPLE

with(numtheory);
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:


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 3almost primes), A111176 (Sophie Germain 4almost primes), A211162 (Sophie Germain 5almost primes).


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



