A154553 Lesser of two consecutive primes, p < q, such that both p*q+p-q and p*q-p+q are prime numbers.

2, 3, 23, 503, 991, 1381, 1621, 3301, 4211, 5471, 5683, 6563, 6581, 7351, 7369, 7829, 8179, 8849, 10061, 11299, 11789, 13841, 14389, 15823, 16981, 17839, 18199, 20563, 21089, 24151, 24989, 25321, 25609, 26203, 28001, 28403, 28433, 32003, 35671

Offset

1,1

Comments

2*3-1=5;2*3+1=7, 3*5-2=13;3*5+2=17, ...

Links

Paolo P. Lava, Table of n, a(n) for n = 1..200

Maple

with(numtheory); A154553:=proc(q) local a, b, n;
for n from 42676 to q do a:=ithprime(n); b:=nextprime(a);
if isprime(a*b+a-b) and isprime(a*b-a+b) then print(a);
fi; od; end: A154553(10^9); # Paolo P. Lava, May 14 2013

Mathematica

lst={}; Do[p=Prime[n]; pn=Prime[n+1]; d=pn-p; If[PrimeQ[p*pn-d]&&PrimeQ[p*pn+d], AppendTo[lst, p]], {n, 8!}]; lst
pnQ[{p_, q_}]:=And@@PrimeQ[{p*q+p-q, p*q-p+q}]; Transpose[Select[ Partition[ Prime[Range[4000]], 2, 1], pnQ]][[1]] (* Harvey P. Dale, Jul 12 2012 *)

Crossrefs

Cf. A138111, A138170, A154550, A154551, A154552

Sequence in context: A104458 A191859 A289550 * A160341 A092388 A225726

Adjacent sequences: A154550 A154551 A154552 * A154554 A154555 A154556

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 11 2009

Extensions

Edited by Omar E. Pol, Jan 12 2009

Status

approved