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A393602
a(n) is the first positive number that is the sum of a prime and the reverse of a prime in exactly n ways.
1
1, 4, 5, 10, 19, 16, 34, 48, 90, 84, 78, 126, 108, 150, 120, 114, 171, 138, 144, 165, 186, 210, 198, 204, 324, 330, 348, 402, 432, 462, 408, 384, 375, 786, 750, 855, 762, 744, 768, 795, 765, 774, 804, 858, 1354, 1050, 792, 1065, 954, 960, 1002, 1467, 984, 978, 1116, 1020, 1245, 1125, 1206, 1521
OFFSET
0,2
COMMENTS
a(n) is the least k such that there are exactly n solutions to k = A000040(i) + A074895(j) = k.
LINKS
FORMULA
A391563(a(n)) = n.
EXAMPLE
a(4) = 19 because 19 = 2 + 17 = 3 + 16 = 5 + 14 = 17 + 2 where 2, 3, 5, 17 are primes and 17, 16, 14, 2 are reverses of the primes 71, 61, 41 and 2.
MAPLE
rev:= proc(n) local L, i; L:= convert(n, base, 10); add(L[-i]*10^(i-1), i=1..nops(L)) end proc:
P:= select(isprime, [2, seq(i, i=3..10^4, 2)]): PR:= sort(map(rev, P)): m:= nops(P):
V:= Vector(10^4):
for i from 1 to m do
for j from 1 to m do
v:= P[i]+PR[j]; if v > 10^4 then break fi;
V[v]:= V[v]+1
od od:
W:= Array(0..200):
for i from 1 to 10^4 do
if V[i] <= 200 and W[V[i]] = 0 then W[V[i]]:= i fi
od:
convert(W, list);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robert Israel, Feb 23 2026
STATUS
approved