A357098 Emirps p such that the average of p and its digit reversal is an emirp.

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

Offset

1,1

Comments

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.

Links

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

Example

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.

Maple

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;

Mathematica

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 *)

Crossrefs

Cf. A006567.

Sequence in context: A096212 A065325 A245210 * A250698 A250683 A065326

Adjacent sequences: A357095 A357096 A357097 * A357099 A357100 A357101

Keyword

nonn,base

Author

Robert Israel, Sep 11 2022

Status

approved