A176804 Lesser of twin primes p such that p = semiprime(k)/2 and p + 2 = semiprime(k+2)/2 for some integer k.

3, 11, 17, 41, 179, 197, 239, 281, 311, 419, 431, 461, 521, 599, 641, 821, 827, 857, 1019, 1049, 1061, 1091, 1151, 1229, 1289, 1319, 1427, 1481, 1487, 1607, 1667, 1697, 1721, 1871, 1877, 1931, 1997, 2027, 2081, 2111, 2141, 2309, 2339, 2591, 2687, 2789

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 26 2010

Keywords

• nonn

Examples

			3 is a term because 3 = semiprime(2)/2 = 6/2 and 3 + 2 = 5 = semiprime(2+2)/2 = 10/2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Maple

From R. J. Mathar, Apr 27 2010: (Start)
isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
A001358 := proc(n) option remember ; if n = 1 then 4; else for a from procname(n-1)+1 do if isA001358(a) then return a; end if; end do: end if ; end proc:
A174956 := proc(p) for n from 1 do if A001358(n) = p then return n; elif A001358(n) > p then return 0 ; end if; end do: end proc:
A001359 := proc(n) option remember; if n = 1 then 3; else for a from procname(n-1)+2 by 2 do if isprime(a) and isprime(a+2) then return a; end if; end do: end if; end proc:
for i from 1 to 400 do p := A001359(i) ; n := A174956(2*p) ; n2 := A174956(2*p+4) ; if n > 0 and n2 >0 and n2=n+2 then printf("%d,",p) ; end if; end do: (End)

Mathematica

(Select[Partition[Select[Range[6000],PrimeOmega[#]==2&],3,1],AllTrue[ {#[[1]]/2 ,#[[3]]/2},PrimeQ]&&#[[3]]-#[[1]]==4&]/2)[[All,1]] (* Harvey P. Dale, Sep 24 2022 *)

Extensions

Corrected (541 replaced by 521, 1047 replaced by 1049, 1741 replaced by 1721) by R. J. Mathar, Apr 27 2010