A379138 a(n) is the first number that is the sum of two palindromic primes in exactly n ways.

0, 4, 10, 504, 25242, 1110, 28782, 46764, 46254, 86058, 50094, 47874, 107880, 108180, 110100, 108990, 107070, 109800, 2726262, 2830272, 2698962, 3029292, 2900982, 2799972, 2979792, 3100002, 2998992, 4498944, 4409034, 4709064, 4510044, 4916184, 4790874, 4787874, 4869684, 4959594, 4896984, 4891884

Offset: 0

Author

Robert Israel, Dec 15 2024

Keywords

• nonn

Comments

a(n) is the least k such that there are exactly n numbers j <= k/2 where both j and k - j are in A002385.

Examples

			a(5) = 1110 because 1110 = 181 + 929 = 191 + 919 = 313 + 797 = 353 + 757 = 383 + 727 is the sum of two palindromic primes in exactly 5 ways, and no smaller even number works.
		

Crossrefs

Cf. A002385, A377848.

Programs

Maple

digrev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
F:= proc(d) # d-digit odd palindromic primes, d >= 3
  local R,x,rx,i;
    select(isprime,map(t -> seq(10^((d+1)/2)*t + i*10^((d-1)/2) + digrev(t),i=0..9), [$(10^((d-3)/2)) .. 10^((d-1)/2)-1]))
end proc:
PP:= [3,5,7,11,op(F(3)),op(F(5)),op(F(7))]: nPP:= nops(PP):
V:= Vector(2*PP[-1],datatype=integer[1]):
for i from 1 to nPP do for j from 1 to i do
   x:= PP[i]+PP[j];
   V[x]:= V[x]+1
od od:
M:= max(V):
W:= Array(0..M,-1):
W[0]:= 0: W[1]:= 4:
for x from 1 to 2*PP[-1] do
  if W[V[x]] = -1 then W[V[x]]:= x fi
od:
convert(W,list); # entries of -1 indicate values > 10^8