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A082769 a(n) = smallest palindromic prime that begins with A082768(n), or 0 if no such number exists.

%I A082769 #7 Aug 27 2025 09:32:58
%S A082769 11,3,7,919,101,11,12421,131,14341,151,16061,17471,181,191,30103,313,
%T A082769 32323,33533,34543,353,36263,373,383,39293,70207,71317,727,73037,
%U A082769 74047,757,76367,77377,787,797,90709,919,929,93139,94049,95959,96269,97379,98389,9902099,1003001,101,1022201,10301,1043401,10501,10601,1074701,1082801,1092901
%N A082769 a(n) = smallest palindromic prime that begins with A082768(n), or 0 if no such number exists.
%C A082769 Conjecture: no entry is zero.
%p A082769 ispali := proc(n,b)
%p A082769     local dgs,i ;
%p A082769     dgs := convert(n,base,b) ;
%p A082769     for i from 1 to nops(dgs)/2 do
%p A082769         if op(i,dgs) <> op(-i,dgs) then
%p A082769             return false;
%p A082769         end if;
%p A082769     end do:
%p A082769     true;
%p A082769 end proc:
%p A082769 L082768 := [seq(A082768(n),n=1..200)] ; # use code in A082768
%p A082769 L082769 := [seq(0,n=1..200)] ;
%p A082769 for pi from 2 do
%p A082769     p :=ithprime(pi) ;
%p A082769     if ispali(p,10) then
%p A082769         pdgs := convert(p,base,10) ;
%p A082769         for sh from 0 do
%p A082769             restp := add(op(i,pdgs)*10^(i-1),i=1..nops(pdgs)) ;
%p A082769             for i from 1 to nops(L082768) do
%p A082769                 if op(i,L082768) = restp then
%p A082769                     if op(i,L082769) = 0 then
%p A082769                         L082769 := subsop(i=p,L082769) ;
%p A082769                         print(L082769) ;
%p A082769                     end if;
%p A082769                 end if;
%p A082769             end do:
%p A082769             # chop digits from palindromic prime starting at least signif
%p A082769             pdgs := subsop(1=NULL,pdgs) ;
%p A082769             if nops(pdgs) = 0 then
%p A082769                 break ;
%p A082769             end if;
%p A082769         end do:
%p A082769     end if;
%p A082769 end do: # _R. J. Mathar_, Aug 27 2025
%Y A082769 Cf. A082768, A082770.
%K A082769 base,nonn,changed
%O A082769 1,1
%A A082769 _Amarnath Murthy_, Apr 18 2003
%E A082769 More terms from _David Wasserman_, Jul 28 2005
%E A082769 12 more terms from _R. J. Mathar_, Aug 27 2025