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A107423
Numbers k equal prime(m)*prime(m+1) such that k+1 is a square and k-1 is an even semiprime.
1
15, 35, 143, 899, 1763, 5183, 19043, 79523, 213443, 359999, 412163, 685583, 777923, 1192463, 1695203, 2585663, 4536899, 5143823, 5673923, 7225343, 12446783, 12659363, 12830723, 17040383, 17892899, 18818243, 20684303, 25100099
OFFSET
1,1
LINKS
EXAMPLE
a(1)=15 because 3*5=15: 15+1=4^2 and 15-1=2*7;
a(2)=35 because 5*7=35: 35+1=6^2 and 35-1=2*17;
a(3)=143 because 11*13=143: 143+1=12^2 and 143-1=2*71;
a(4)=899 because 29*31=899: 899+1=30^2 and 899-1=2*449;
MAPLE
Res:= NULL: count:= 0:
q:= 2:
while count < 100 do
p:= q; q:= nextprime(p);
k:= p*q;
if issqr(k+1) and isprime((k-1)/2) then
count:= count+1; Res:= Res, k;
fi
od:
Res; # Robert Israel, Feb 12 2026
CROSSREFS
Sequence in context: A194580 A210503 A037074 * A027442 A208728 A219689
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto, May 26 2005
EXTENSIONS
Terms beyond a(6) from R. J. Mathar, Jun 28 2010
STATUS
approved