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A357098
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Emirps p such that the average of p and its digit reversal is an emirp.
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1
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1001941, 1008701, 1012481, 1012861, 1034861, 1035641, 1037081, 1040981, 1052041, 1060781, 1078001, 1092061, 1101571, 1101931, 1102571, 1124951, 1141391, 1142131, 1142171, 1146791, 1149131, 1152071, 1157491, 1161331, 1165991, 1171231, 1185791, 1256681, 1267381, 1312411, 1319411, 1321571, 1321711
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OFFSET
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1,1
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COMMENTS
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All terms have an odd number of digits, because if x has an even number of digits, the average of x and its digit reversal is divisible by 11.
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LINKS
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EXAMPLE
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a(3) = 1012481 is a term because 1012481 is an emirp (i.e., it and its digit reversal 1842101 are distinct primes) and the average of 1012481 and 1842101 is 1427291, which is an emirp.
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MAPLE
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rev:= proc(n) local L, i;
L:= convert(n, base, 10);
add(10^(i-1)*L[-i], i=1..nops(L))
end proc:
isemirp:= proc(n) local r;
if not isprime(n) then return false fi;
r:= rev(n);
r <> n and isprime(r)
end proc:
filter:= proc(n) local t, r, L, i;
if not isprime(n) then return false fi;
r:= rev(n);
r <> n and isprime(r) and isemirp((n+r)/2)
end proc:
count:= 0: R:= NULL:
for m from 2 by 2 while count < 100 do
for d1 in [1, 3, 7, 9] while count < 100 do
for nn from d1*10^m+1 to (d1+1)*10^m by 2 while count < 100 do
if filter(nn) then count:= count+1; R:= R, nn fi
od od od:
R;
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MATHEMATICA
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emirpQ[n_] := (r = IntegerReverse[n]) != n && And @@ PrimeQ[{n, r}]; Select[Range[1350000], OddQ[IntegerLength[#]] && EvenQ[s = # + IntegerReverse[#]] && emirpQ[#] && emirpQ[s/2] &] (* Amiram Eldar, Sep 11 2022 *)
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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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