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A356947 Emirps p such that p == 1 (mod s) and R(p) == 1 (mod s), where R(p) is the digit reversal of p and s the sum of digits of p. 2
1021, 1031, 1201, 1259, 1301, 9521, 10253, 10711, 11071, 11161, 11243, 11701, 12113, 12241, 14221, 15907, 16111, 16481, 17011, 17491, 18461, 19471, 30757, 31121, 34211, 35201, 70951, 71347, 71569, 72337, 73327, 74317, 75703, 96517, 100621, 101611, 101701, 102061, 102913, 103141, 105211, 106661 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Emirps p such that p and its digit reversal are quasi-Niven numbers.
LINKS
EXAMPLE
a(3) = 1201 is a term because it and its digit reversal 1021 are distinct primes with sum of digits 4, and 1201 == 1021 == 1 (mod 4).
MAPLE
filter:= proc(n) local L, i, r, s;
if not isprime(n) then return false fi;
L:= convert(n, base, 10);
r:= add(L[-i]*10^(i-1), i=1..nops(L));
if r = n or not isprime(r) then return false fi;
s:= convert(L, `+`);
n mod s = 1 and r mod s = 1
end proc:
select(filter, [seq(i, i=13 .. 200000, 2)]);
MATHEMATICA
Select[Range[110000], (r = IntegerReverse[#]) != # && PrimeQ[#] && PrimeQ[r] && Divisible[# - 1, (s = Plus @@ IntegerDigits[#])] && Divisible[r - 1, s] &] (* Amiram Eldar, Sep 06 2022 *)
PROG
(Python)
from sympy import isprime
def ok(n):
strn = str(n)
R, s = int(strn[::-1]), sum(map(int, strn))
return n != R and n%s == 1 and R%s == 1 and isprime(n) and isprime(R)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Sep 06 2022
CROSSREFS
Sequence in context: A303918 A371378 A228625 * A214732 A088290 A209620
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Sep 05 2022
STATUS
approved

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Last modified April 20 15:37 EDT 2024. Contains 371844 sequences. (Running on oeis4.)