The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A357098 Emirps p such that the average of p and its digit reversal is an emirp. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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: A357094 A357095 A357096 * A357099 A357100 A357101 KEYWORD nonn,base AUTHOR Robert Israel, Sep 11 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 31 17:49 EST 2023. Contains 359980 sequences. (Running on oeis4.)