A183058 - OEIS

%I #11 Jun 06 2020 17:20:39

%S 509,809,12011,12041,13049,14081,16091,18041,21011,21089,22013,22079,

%T 23099,25073,28019,29021,29033,31019,33023,33053,35069,35081,35099,

%U 36083,37013,37049,38039,39089,41081,42023,42071,42089,43013

%N Cyclops Sophie-Germain primes.

%C Sophie Germain primes which are also Cyclops numbers.

%H Harvey P. Dale, <a href="/A183058/b183058.txt">Table of n, a(n) for n = 1..2000</a>

%F A005384 INTERSECT A134808.

%e 509 is in the sequence because 509 is a Sophie Germain prime A005384 and it is also a Cyclops number A134808.

%p isA005384 := proc(n) isprime(n) and isprime(2*n+1) ; end proc:

%p 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:

%p isA183058 := proc(n) isA005384(n) and isA134808(n) ; end proc:

%p for n from 0 to 50000 do if isA183058(n) then printf("%d,",n); end if; end do: # _R. J. Mathar_, Jan 05 2011

%t 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 *)

%Y Cf. A005384, A134808, A134809, A136098, A153807, A183059.

%K nonn,base

%O 1,1

%A _Omar E. Pol_, Dec 26 2010