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

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

Offset: 1

Author

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

Keywords

• base
• fini
• full
• nonn

Comments

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..78

Crossrefs

Cf. A002385, A082620, A082621, A082622, A082624.

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