cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A081939 a(1) = 2; a(n+1) is the smallest palindrome > a(n) that has a common factor with a(n).

Original entry on oeis.org

2, 4, 6, 8, 22, 33, 44, 55, 66, 77, 88, 99, 111, 141, 171, 222, 232, 242, 252, 262, 272, 282, 292, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 585, 595, 616, 626, 636, 646, 656, 666, 676, 686, 696, 717, 747, 777, 828, 838, 848, 858, 868, 878, 888, 898
Offset: 1

Views

Author

Amarnath Murthy, Apr 02 2003

Keywords

Comments

Palindromes with an even number of digits are divisible by 11, so when a(n)=A002113(k) and A055642(a(n)) and A055642(A002113(k+1)) are even, a(n+1)=A002113(k+1). - Robert Israel, Jul 04 2018

Links

Crossrefs

Cf. A002113, A055642, A083136, A081938.

Programs

  • Maple
    dmax:= 5: # to get all terms with at most dmax digits
revdigs:= proc(n)
  local L, Ln, i;
  L:= convert(n, base, 10);
  Ln:= nops(L);
  add(L[i]*10^(Ln-i), i=1..Ln);
end proc:
P:= $0..9:
for d from 2 to dmax do
  if d::even then
    P:= P, seq(10^(d/2)*x + revdigs(x), x=10^(d/2-1)..10^(d/2)-1)
  else
    m:= (d-1)/2;
    P:= P, seq(seq(10^(m+1)*x + 10^m*j+revdigs(x), j=0..9),x=10^(m-1)..10^m-1);
  fi
od:
P:= [P]:
r:= P[3]: Res:= r: count:= 1:
for i from 4 to nops(P) do
  if igcd(P[i],r) > 1 then
    count:= count+1; r:= P[i]; Res:= Res, r;
  fi
od:
Res; # Robert Israel, Jul 04 2018
  • PARI
    ispal(n) = my(d=digits(n)); d == Vecrev(d);
lista(nn) = {print1(last = 2, ", "); for (n=3, nn, if (ispal(n) && (gcd(n, last) != 1), print1(n, ", "); last = n;););} \\ Michel Marcus, Aug 12 2015

Extensions

More terms from David Wasserman, Jun 29 2004

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

Original entry on oeis.org

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

Views

Author

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

Keywords

Comments

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

Links

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

A083139 Primes in A083137.

Original entry on oeis.org

2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 25 2003

Keywords

Comments

Conjecture: sequence is infinite.
Does this coincide with A002385? It seems possible that the answer is no, since some palindromic primes may be missed in A083137. - Andrew S. Plewe and N. J. A. Sloane, May 14 2007

Links

Crossrefs

Cf. A083136, A083137, A083138.
Cf. A069217. - R. J. Mathar, Sep 17 2008

Extensions

More terms from Reinhard Zumkeller, May 05 2003

A083138 Composite numbers in A083137.

Original entry on oeis.org

323, 767, 989, 10001, 11111, 13031, 14141, 14941, 15151, 17371, 32023, 33233, 34343, 36763, 71017, 73937, 74147, 74947, 77177, 77677, 78587, 90109, 92629, 94249, 1006001, 1013101, 1024201, 1033301, 1047401, 1049401, 1066601, 1073701
Offset: 1

Views

Author

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

Keywords

Crossrefs

Cf. A002113, A083136, A083139.

Extensions

Corrected and extended by Reinhard Zumkeller, May 05 2003
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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