A345408 Numbers that are the sum of an emirp and its reversal in more than one way.

1090, 2662, 2992, 3212, 4334, 4994, 5104, 5324, 6776, 7106, 9328, 9548, 10450, 10670, 10780, 11110, 11330, 11440, 11660, 12122, 12452, 12892, 13222, 15004, 16786, 17446, 17666, 29092, 29482, 31912, 36352, 44644, 44834, 45454, 46654, 46664, 47474, 47864, 49094, 49294, 49484, 49684, 49894, 50104

Offset: 1

Author

J. M. Bergot and Robert Israel, Jun 18 2021

Keywords

• nonn
• base

Comments

Numbers that are in A345409 in more than one way.

Interchanging an emirp and its reversal is not counted as a different way.

Examples

			a(3) = 2992 is a member because 2992 = 1091 + 1901 = 1181+1811 where 1091 and 1181 and their reversals 1901 and 1811 are primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006567, A345409.

Programs

Maple

revdigs:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:
isemirp1:= proc(n) local r;
if not isprime(n) then return false fi;
r:= revdigs(n);
r > n and isprime(r)
end proc:
E:= select(isemirp1, [seq(seq(seq(i*10^d+j,j=1..10^d-1,2),i=[1,3,7,9]),d=1..4)]):
V:= sort(map(t -> t+revdigs(t),E)):
M:= select(t -> V[t+1]=V[t], [$1..nops(V)-1]):
sort(convert(convert(V[M],set),list));

Python

from collections import Counter
from sympy import isprime, nextprime
def epgen(start=1, end=float('inf')): # generates unique emirp/prime pairs
    p = nextprime(start-1)
    while p <= end:
        revp = int(str(p)[::-1])
        if p < revp and isprime(revp): yield (p, revp)
        p = nextprime(p)
def aupto(lim):
    c = Counter(sum(ep) for ep in epgen(1, lim) if sum(ep) <= lim)
    return sorted(s for s in c if c[s] > 1)
print(aupto(50105)) # Michael S. Branicky, Jun 18 2021