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A145351 Prime-indexed composites k such that lpf(k) + gpf(k) is a prime. 1
6, 10, 20, 22, 30, 44, 54, 58, 66, 82, 96, 108, 120, 136, 142, 144, 204, 232, 324, 330, 340, 352, 384, 464, 492, 544, 596, 616, 704, 738, 750, 792, 870, 894, 918, 960, 990, 1062, 1234, 1312, 1318, 1326, 1498, 1534, 1540, 1566, 1576, 1632, 1694, 1700, 1722 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
6 is a term because it is the 2nd composite number, 6=2*3, and 2+3=5 is prime;
10 is a term because it is the 5th composite number, 10=2*5, and 2+5=7 is prime;
22 is a term because it is the 13th composite number, 22=2*11, and 2+11=13 is prime;
44 is a term because it is the 29th composite number, 44=2*2*11, and 2+11=13 is prime.
MAPLE
A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:
A002808 := proc(n) if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do: end if; end proc:
A065858 := proc(n) A002808(ithprime(n)) ; end proc:
A145351 := proc(n) c := A065858(n) ; if isprime(A020639(c) + A006530(c)) then printf("%d, ", c) ; end if; end proc:
seq(A145351(n), n=1..400) ; # R. J. Mathar, May 01 2010
MATHEMATICA
pfiQ[n_]:=Module[{f=FactorInteger[n]}, PrimeQ[f[[1, 1]]+f[[-1, 1]]]]; Module[ {nn=2000, c}, c=Select[ Range[nn], CompositeQ]; Select[ Table[ Take[c, {n}][[1]], {n, Prime[Range[PrimePi[Length[c]]]]}], pfiQ]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 18 2019 *)
CROSSREFS
Cf. A000040, A002808, A020639 (lpf), A006530 (gpf).
Sequence in context: A095985 A270306 A327410 * A227874 A015783 A356055
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected (inserted 20 from n=5, 30 from n=8, removed 200) and extended beyond 204 by R. J. Mathar, May 01 2010
Edited by Jon E. Schoenfield, Feb 07 2019
STATUS
approved

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Last modified May 22 19:06 EDT 2024. Contains 372758 sequences. (Running on oeis4.)