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
Keywords
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.
Programs
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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
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