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Lesser emirps (A109308) subtracted from their reversals.
1

%I #52 Dec 28 2023 16:12:07

%S 18,54,36,18,594,198,792,594,594,792,792,396,396,594,594,198,198,198,

%T 7992,180,270,2268,540,8532,810,6804,1908,7902,360,2358,630,2718,1908,

%U 5904,1998,7992,90,6084,8172,8262,8442,2538,450,8532,7632,7812,7902,2088,270

%N Lesser emirps (A109308) subtracted from their reversals.

%H Robert Israel, <a href="/A346756/b346756.txt">Table of n, a(n) for n = 1..10000</a>

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_020.htm">Puzzle 20. Reversible Primes</a>, The Prime Puzzles and Problems Connection.

%F a(n) = reverse(A109308(n)) - A109308(n).

%e 31 - 13 = 18, 71 - 17 = 54, 73 - 37 = 36 (distance between lesser emirps and their reversals).

%p rev:= proc(n) local L,i;

%p L:= convert(n,base,10);

%p add(L[-i]*10^(i-1),i=1..nops(L));

%p end proc:

%p f:= proc(p) local r;

%p if not isprime(p) then return NULL fi;

%p r:= rev(p);

%p if r > p and isprime(r) then r-p else NULL fi

%p end proc:

%p map(f, [seq(i,i=11 .. 10^4, 2)]); # _Robert Israel_, Dec 28 2023

%t f[n_] := IntegerReverse[n] - n; Map[f, Select[Range[1500], f[#] > 0 && PrimeQ[#] && PrimeQ @ IntegerReverse[#] &]] (* _Amiram Eldar_, Sep 08 2021 *)

%o (PARI) rev(p) = fromdigits(Vecrev(digits(p))); \\ A004086

%o lista(nn) = {my(list = List()); forprime (p=1, nn, my(q=rev(p)); if ((q>p) && isprime(q), listput(list, q-p));); Vec(list);} \\ _Michel Marcus_, Sep 07 2021

%o (Python)

%o from sympy import isprime, nextprime

%o def aupton(terms):

%o alst, p = [], 2

%o while len(alst) < terms:

%o revp = int(str(p)[::-1])

%o if p < revp and isprime(revp):

%o alst.append(revp - p)

%o p = nextprime(p)

%o return alst

%o print(aupton(49)) # _Michael S. Branicky_, Sep 08 2021

%Y Cf. A004086, A006567, A109308.

%K nonn,base,look

%O 1,1

%A _George Bull_, Aug 20 2021

%E Better name and more terms from _Jon E. Schoenfield_, Aug 20 2021