A183058 Cyclops Sophie-Germain primes.

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

Offset: 1

Author

Omar E. Pol, Dec 26 2010

Keywords

• nonn
• base

Comments

Sophie Germain primes which are also Cyclops numbers.

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2000

Crossrefs

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

Programs

Maple

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

Mathematica

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 *)

Formula

A005384 INTERSECT A134808.