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A176804
Lesser of twin primes p such that p = semiprime(k)/2 and p + 2 = semiprime(k+2)/2 for some integer k.
1
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
1,1
LINKS
EXAMPLE
3 is a term because 3 = semiprime(2)/2 = 6/2 and 3 + 2 = 5 = semiprime(2+2)/2 = 10/2.
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 *)
CROSSREFS
Sequence in context: A100567 A270225 A262275 * A078116 A245045 A127996
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected (541 replaced by 521, 1047 replaced by 1049, 1741 replaced by 1721) by R. J. Mathar, Apr 27 2010
STATUS
approved