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A183058
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Cyclops Sophie-Germain primes.
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2
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509, 809, 12011, 12041, 13049, 14081, 16091, 18041, 21011, 21089, 22013, 22079, 23099, 25073, 28019, 29021, 29033, 31019, 33023, 33053, 35069, 35081, 35099, 36083, 37013, 37049, 38039, 39089, 41081, 42023, 42071, 42089, 43013
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OFFSET
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1,1
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COMMENTS
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Sophie Germain primes which are also Cyclops numbers.
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LINKS
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FORMULA
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EXAMPLE
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509 is in the sequence because 509 is a Sophie Germain prime A005384 and it is also a Cyclops number A134808.
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MAPLE
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isA005384 := proc(n) isprime(n) and isprime(2*n+1) ; end proc:
isA134808 := proc(n) local dgs, ndgs; dgs := convert(n, base, 10) ; mdg := (nops(dgs)+1)/2 ; if type(nops(dgs), 'even') then false; elif n = 0 then true; else if op(mdg, dgs) <> 0 then false; else if mul(op(k, dgs), k=1..mdg-1) =0 or mul(op(k, dgs), k=mdg+1..nops(dgs)) = 0 then false; else true; end if; end if; end if; end proc:
isA183058 := proc(n) isA005384(n) and isA134808(n) ; end proc:
for n from 0 to 50000 do if isA183058(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Jan 05 2011
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MATHEMATICA
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csgpQ[n_]:=Module[{idn=IntegerDigits[n], len}, len=Length[idn]; PrimeQ[2n+1]&&OddQ[len]&&idn[[(len+1)/2]]==0&&Count[idn, 0]==1]; Select[Prime[ Range[ 4500]], csgpQ] (* Harvey P. Dale, Jun 06 2020 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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