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

11, 3, 7, 919, 101, 11, 12421, 131, 14341, 151, 16061, 17471, 181, 191, 30103, 313, 32323, 33533, 34543, 353, 36263, 373, 383, 39293, 70207, 71317, 727, 73037, 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

Offset: 1

Author

Amarnath Murthy, Apr 18 2003

Keywords

• base
• nonn
• changed

Comments

Conjecture: no entry is zero.

Crossrefs

Cf. A082768, A082770.

Programs

Maple

ispali := proc(n,b)
    local dgs,i ;
    dgs := convert(n,base,b) ;
    for i from 1 to nops(dgs)/2 do
        if op(i,dgs) <> op(-i,dgs) then
            return false;
        end if;
    end do:
    true;
end proc:
L082768 := [seq(A082768(n),n=1..200)] ; # use code in A082768
L082769 := [seq(0,n=1..200)] ;
for pi from 2 do
    p :=ithprime(pi) ;
    if ispali(p,10) then
        pdgs := convert(p,base,10) ;
        for sh from 0 do
            restp := add(op(i,pdgs)*10^(i-1),i=1..nops(pdgs)) ;
            for i from 1 to nops(L082768) do
                if op(i,L082768) = restp then
                    if op(i,L082769) = 0 then
                        L082769 := subsop(i=p,L082769) ;
                        print(L082769) ;
                    end if;
                end if;
            end do:
            # chop digits from palindromic prime starting at least signif
            pdgs := subsop(1=NULL,pdgs) ;
            if nops(pdgs) = 0 then
                break ;
            end if;
        end do:
    end if;
end do: # R. J. Mathar, Aug 27 2025

Extensions

More terms from David Wasserman, Jul 28 2005

12 more terms from R. J. Mathar, Aug 27 2025