A345409 Numbers that are the sum of an emirp and its reversal.

44, 88, 110, 176, 424, 808, 908, 928, 1070, 1090, 1150, 1190, 1312, 1372, 1616, 1676, 1736, 2222, 2332, 2552, 2662, 2992, 3212, 4114, 4334, 4444, 4664, 4774, 4994, 5104, 5324, 5434, 6226, 6776, 6886, 7106, 7436, 8338, 8558, 8998, 9218, 9328, 9548, 10010, 10120, 10450, 10670, 10780, 11000, 11110

Offset: 1

Author

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

Keywords

• nonn

Examples

			a(3) = 110 is a member because 110 = 37+73 where 37 is an emirp.
		

Links

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

Crossrefs

Cf. A006567, A345408.

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:
f:= proc(n) local r;
if not isprime(n) then return NULL fi;
r:= revdigs(n);
if r > n and isprime(r) then return r+n fi
end proc:
S:= map(f, {seq(seq(seq(i*10^d+j,j=1..10^d-1,2),i=[1,3,7,9]),d=1..4)}):
sort(convert(S,list));

Python

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):
    epsums = set(sum(ep) for ep in epgen(1, lim))
    return sorted(filter(lambda x: x<=lim, epsums))
print(aupto(11111)) # Michael S. Branicky, Jun 18 2021