A050784 - OEIS

%I #16 Aug 19 2021 06:41:31

%S 2,3,5,7,101,131,151,181,191,313,353,373,383,727,757,787,797,919,929,

%T 10301,10501,10601,12421,12721,12821,13831,13931,14341,14741,15451,

%U 16061,16361,16561,17471,17971,18181,18481,19391,19891,30103,30203

%N Palindromic primes containing no pair of consecutive equal digits.

%H Robert Israel, <a href="/A050784/b050784.txt">Table of n, a(n) for n = 1..10000</a>

%p nextL:= proc(L) local V,j,n,k;

%p   n:= LinearAlgebra:-Dimension(L);

%p   V:= L;

%p   for j from n to 1 by -1 do

%p     V[j]:= V[j]+1;

%p     if j > 1 then if V[j] = V[j-1] then V[j]:= V[j]+1 fi

%p     elif member(V[j],[2,8]) then V[j]:= V[j]+1

%p     elif member(V[j],[4,5,6]) then V[j]:= 7

%p     fi;

%p     if V[j] <= 9 then

%p       for k from j+1 to n do if (k-j)::odd then V[k]:= 0 else V[k]:= 1 fi od;

%p       return V

%p     fi;

%p   od;

%p   Vector(n+1, i -> i mod 2)

%p end proc:

%p Pali:= proc(L)

%p   local i,n;

%p   n:= LinearAlgebra:-Dimension(L);

%p   add(L[i]*10^(2*n-i-1),i=1..n)+add(L[i]*10^(i-1),i=1..n-1)

%p end proc:

%p V:= <5>: Res:= 2,3,5: count:= 3:

%p while count < 100 do

%p   V:= nextL(V);

%p   x:= Pali(V);

%p   if isprime(x) then count:= count+1; Res:= Res, x fi;

%p od:

%p Res; # _Robert Israel_, Feb 07 2019

%t Select[Prime[Range[3280]],Reverse[x=IntegerDigits[#]]==x&&FreeQ[Differences[x],0]&] (* _Jayanta Basu_, Jun 01 2013 *)

%Y Cf. A002385, A050783, A030147, A050757, A046075.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Sep 15 1999