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

1,1

Links

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

Example

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

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));

Prog

(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

Crossrefs

Cf. A006567, A345408.

Sequence in context: A195816 A118087 A335481 * A246412 A248365 A044182

Adjacent sequences: A345406 A345407 A345408 * A345410 A345411 A345412

Keyword

nonn

Author

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

Status

approved