A136098 -id:A136098 - cp's OEIS frontend

A138131 Palindromic cyclops numbers.

0, 101, 202, 303, 404, 505, 606, 707, 808, 909, 11011, 12021, 13031, 14041, 15051, 16061, 17071, 18081, 19091, 21012, 22022, 23032, 24042, 25052, 26062, 27072, 28082, 29092, 31013, 32023, 33033, 34043, 35053, 36063, 37073, 38083

Offset: 1

Omar E. Pol, Mar 09 2008

For prime entries in the sequence see A136098. - Lekraj Beedassy, Mar 15 2008, May 21 2008

			101 is a member because 101 is a palindromic number A002113 and also a cyclops number A134808.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A002113, A002385, A134808.

f:= proc(n,d) local L,m,k;
  L:= convert(9^d+n,base,9);
  add((1+L[d+1-i])*(10^(i-1)+10^(2*d+1-i)),i=1..d)
end proc:
seq(seq(f(n,d),n=0..9^d-1),d=0..2); # Robert Israel, Feb 18 2018

Join[{0},Flatten[Table[Select[Range[10^(2n),10^(2n+1)-1],PalindromeQ[ #] && DigitCount[ #,10,0]==1&&IntegerDigits[#][[(IntegerLength[#]+1)/2]]==0&],{n,2}]]] (* Harvey P. Dale, Dec 03 2022 *)

A183058 Cyclops Sophie-Germain primes.

Original entry on oeis.org

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

Omar E. Pol, Dec 26 2010

Sophie Germain primes which are also Cyclops numbers.

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

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

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

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

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 *)

A005384 INTERSECT A134808.

cp's OEIS Frontend

A138131 Palindromic cyclops numbers.

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