A176804 - OEIS

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

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OFFSET

1,1

LINKS

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

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

Adjacent sequences: A176801 A176802 A176803 * A176805 A176806 A176807

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Apr 26 2010

EXTENSIONS

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

STATUS

approved