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.

A082622 a(1) = 3, a(n) = smallest palindromic prime obtained by inserting two paired digits anywhere in a(n-1).

Original entry on oeis.org

3, 131, 10301, 1003001, 100030001, 10070307001, 1000703070001, 100075030570001, 10006750305760001, 1000167503057610001, 100015675030576510001, 10001056750305765010001, 1000105367503057635010001, 100001053675030576350100001, 10000105360750305706350100001
Offset: 1

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Author

Amarnath Murthy, Apr 29 2003

Keywords

Comments

With the exception of 11, all decimal palindromic numbers with an even number of digits are composite (they are divisible by 11). This leaves only odd-digit-length palindromes, therefore (at least) a pair of digits needs to be inserted at every iteration.
The sequence terminates at a(19) = 1000010025136075033305706315200100001, which cannot be extended to another palindromic prime by inserting two paired digits. - Giovanni Resta, Sep 20 2019

Crossrefs

Extensions

Terms following a(6) corrected by Giovanni Resta, Sep 20 2019
Deleted an incorrect program. - N. J. A. Sloane, Dec 05 2024

A082621 a(1) = 2, then the smallest palindromic prime obtained by inserting digits anywhere in a(n-1) (including at the ends).

Original entry on oeis.org

2, 727, 37273, 3072703, 307323703, 30073237003, 3006732376003, 300067323760003, 30000673237600003, 3000067382837600003, 300006738242837600003, 30000673820402837600003, 3000063738204028373600003, 300006373821040128373600003, 30000635738210401283753600003
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 29 2003

Keywords

Crossrefs

Extensions

Corrected by R. J. Mathar, Oct 01 2006
More terms from Giovanni Resta, Sep 20 2019

A082623 a(1) = 5, a(n) = smallest palindromic prime obtained by inserting two digits anywhere in a(n-1).

Original entry on oeis.org

5, 151, 10501, 1035301, 103515301, 10325152301, 1013251523101, 101325181523101, 10132512821523101, 1013251428241523101, 101322514282415223101, 10132245142824154223101, 1013224514281824154223101, 101322451402818204154223101, 10132245014028182041054223101
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 29 2003

Keywords

Comments

a(78) is the last term, as none of the candidates for a(79) is prime. - Giovanni Resta, Sep 20 2019

Crossrefs

Programs

  • Maple
    cp:= proc(x,y) if x[1] < y[1] then true
               elif x[1] > y[1] then false
               elif nops(x)=1 then true
               else procname(x[2..-1],y[2..-1])
               fi
    end proc: A[1]:= 5: L:= [5]:
    for n from 2 to 15 do
      nL:= nops(L);
      Lp:= sort([seq(seq([op(L[1..i]), x, op(L[i+1..-1])], x=`if`(i=0, 1..9, 0..9)), i=0..nL)], cp);
      cands:= map(t -> add(t[i]*(10^(i-1)+10^(2*nL+1-i)), i=1..nL)+t[nL+1]*10^(nL), Lp);
      found:= false;
      for i from 1 to nops(cands) do
        if isprime(cands[i]) then
          A[n]:= cands[i];
          L:= Lp[i];
          found:= true;
          break
        fi
      od;
      if not found then break fi
    od:
    seq(A[i],i=1..15); # Robert Israel, Jan 03 2017, corrected Sep 20 2019

Extensions

Terms after a(4) corrected by Giovanni Resta, Sep 20 2019

A082624 a(1) = 7, a(n) = smallest palindromic prime obtained by inserting digit anywhere in a(n-1).

Original entry on oeis.org

7, 373, 30703, 3007003, 302070203, 30207570203, 3062075702603, 306020757020603, 30602075057020603, 3060320750570230603, 300603207505702306003, 30060320275057202306003, 3006032021750571202306003, 300603202127505721202306003, 30046032021275057212023064003
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 29 2003

Keywords

Crossrefs

Extensions

More terms from Giovanni Resta, Sep 20 2019
Showing 1-4 of 4 results.