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A345408
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Numbers that are the sum of an emirp and its reversal in more than one way.
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3
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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
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OFFSET
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1,1
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COMMENTS
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Numbers that are in A345409 in more than one way.
Interchanging an emirp and its reversal is not counted as a different way.
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LINKS
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EXAMPLE
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a(3) = 2992 is a member because 2992 = 1091 + 1901 = 1181+1811 where 1091 and 1181 and their reversals 1901 and 1811 are primes.
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MAPLE
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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));
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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