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

1,1

Comments

Sophie Germain primes which are also Cyclops numbers.

Links

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

Formula

A005384 INTERSECT A134808.

Example

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

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 *)

Crossrefs

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

Sequence in context: A159686 A198195 A142819 * A256709 A110025 A059763

Adjacent sequences: A183055 A183056 A183057 * A183059 A183060 A183061

Keyword

nonn,base

Author

Omar E. Pol, Dec 26 2010

Status

approved