A083137 Smallest palindromic number relatively prime to all the previous terms.

1, 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 323, 353, 373, 383, 727, 757, 767, 787, 797, 919, 929, 989, 10001, 10301, 10501, 10601, 11111, 11311, 11411, 12421, 12721, 12821, 13031, 13331, 13831, 13931, 14141, 14341, 14741, 14941, 15151, 15451

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 24 2003

Keywords

• base
• nonn

Comments

323 is the first composite entry. Conjecture: sequence is infinite.

Links

• R. J. Mathar and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 966 terms from R. J. Mathar)

Crossrefs

Cf. A002113, A083136, A083139 (primes in this sequence).

Programs

Maple

isA002113 := proc(n)
    if digrev(n) = n then
        true;
    else
        false;
    end if;
end proc:
A083137 := proc(n)
    option remember;
    if n =1 then
        1;
    else
        for p from procname(n-1)+1 do
            if isA002113(p) then
                rpr := true;
                for i from 1 to n-1 do
                    if igcd(procname(i),p) > 1 then
                        rpr := false;
                        break;
                    end if;
                end do:
                if rpr then
                    return p ;
                end if;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Aug 23 2014

Mathematica

a[1] = 1; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, If[PalindromeQ[k] && AllTrue[Array[a, n-1], CoprimeQ[#, k]&], Return[k]]]; Array[a, 50] (* Jean-François Alcover, Jan 17 2018 *)

Extensions

Corrected and extended by Reinhard Zumkeller, May 05 2003