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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 Robert Israel, Table of n, a(n) for n = 1..1000 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 Cf. A004086, A006567, A209871. Sequence in context: A303918 A371378 A228625 * A214732 A088290 A209620 Adjacent sequences: A356944 A356945 A356946 * A356948 A356949 A356950 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.)