A225319 -id:A225319 - cp's OEIS frontend

A227217 Primes p such that p + (product of digits of p) is prime and p - (product of digits of p) is prime.

23, 29, 83, 101, 103, 107, 109, 293, 307, 347, 349, 401, 409, 431, 439, 503, 509, 601, 607, 653, 659, 677, 701, 709, 743, 809, 907, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1123, 1201, 1297, 1301, 1303, 1307, 1409, 1423, 1489, 1523

Offset: 1

Derek Orr, Sep 19 2013

Intersection of A157677 and A225319.

Contains A056709. - Robert Israel, Apr 13 2015

			431 is prime, 431 + (4*3*1) = 443 is prime, and 431 - (4*3*1) = 419 is prime. So, 431 is a term in the sequence.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A007954, A056709, A157677, A225319.

filter:= proc(n) local m;
  if not isprime(n) then return false fi;
  m:= convert(convert(n,base,10),`*`);
  if m = 0 then return true fi;
  isprime(n+m) and isprime(n-m)
end proc:
select(filter, [seq(2*i+1,i=5..10000)]); # Robert Israel, Apr 13 2015

fQ[n_] := Block[{d = IntegerDigits@ n}, PrimeQ[n + Times @@ d] && PrimeQ[n - Times @@ d]]; Select[Prime@ Range@ 250, fQ] (* Michael De Vlieger, Apr 12 2015 *)

forprime(p=1,2000,d=digits(p);P=prod(i=1,#d,d[i]);if(isprime(p+P)&&isprime(p-P),print1(p,", "))) \\ Derek Orr, Apr 10 2015

from sympy import isprime, primerange
def DP(n):
    p = 1
    for i in str(n):
        p *= int(i)
    return p
for pn in primerange(1, 2000):
    dpn = DP(pn)
    if isprime(pn-dpn) and isprime(pn+dpn):
        print(pn, end=', ')
# Simplified by Derek Orr, Apr 10 2015

[p for p in primes_first_n(1000) if ((p-prod(Integer(p).digits(base=10))) in Primes() and (p+prod(Integer(p).digits(base=10))) in Primes())] # Tom Edgar, Sep 19 2013

More terms from Derek Orr, Apr 10 2015

A229176 Primes p with nonzero digits such that p + product_of_digits and p - product_of_digits are both prime.

Original entry on oeis.org

23, 29, 83, 293, 347, 349, 431, 439, 653, 659, 677, 743, 1123, 1297, 1423, 1489, 1523, 1657, 1867, 2239, 2377, 2459, 2467, 2543, 2579, 2663, 2753, 3163, 3253, 3271, 3329, 3457, 3461, 3581, 3691, 3727, 3833, 3947, 3967, 4129, 4253, 4297, 4423, 4567, 4957, 5323, 5381, 5651

Offset: 1

Derek Orr, Sep 30 2013

Numbers with nonzero digits in A227217; the non-degenerate cases, so to speak.

Intersection of primes with nonzero digits in A157677 and A225319.

			743 is prime.
743 - (7*4*3) = 659 is prime.
743 + (7*4*3) = 827 is prime.
So, 743 is a member of this sequence.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A227217, A157677, A225319.

A007954 := proc(n)
    mul(d, d=convert(n, base, 10))
end proc:
isA229176 := proc(n)
    if isprime(n) and A007954(n) <> 0 then
        isprime(n+A007954(n)) and isprime(n-A007954(n))  ;
        simplify(%) ;
    else
        false;
    end if;
end proc:
for n from 1 to 10000 do
    if isA229176(n) then
        printf("%d,",n) ;
    end if;
end do:

id[x_] := IntegerDigits[x]; ti[x_] := Times @@ id[x]; m=5000; Select[Range[3,m,2], PrimeQ[#] && Min[id[#]] > 0 && PrimeQ[#+ti[#]] && PrimeQ[#-ti[#]]&] (* Zak Seidov, Oct 02 2013 *)
t@n_ := Block[{p = Times @@ IntegerDigits@n},
  If[p == 0, {0}, n + {-p, p}]]; Select[Prime@Range@1000,
AllTrue[t@#, PrimeQ] &] (* Hans Rudolf Widmer, Dec 13 2021 *)

forprime(p=1,10^4,d=digits(p);P=prod(i=1,#d,d[i]);if(P&&isprime(p+P)&&isprime(p-P),print1(p,", "))) \\ Derek Orr, Mar 22 2015

import sympy
from sympy import isprime
def DP(n):
  p = 1
  for i in str(n):
    p *= int(i)
  return p
{print(n, end=', ') for n in range(10**4) if DP(n) and isprime(n) and isprime(n+DP(n)) and isprime(n-DP(n))}
# Simplified by Derek Orr, Mar 22 2015

A225677 Primes of the form p - (product of digits of p), where p is a prime.

Original entry on oeis.org

11, 17, 19, 31, 37, 59, 101, 103, 107, 109, 113, 173, 179, 193, 199, 211, 227, 233, 239, 241, 257, 263, 307, 311, 317, 331, 383, 389, 397, 401, 409, 419, 439, 479, 499, 503, 509, 521, 547, 563, 571, 577, 601, 607, 613, 617, 659, 691, 701, 709, 719, 733, 809

Offset: 1

Jayanta Basu, May 12 2013

Primes generated by A225319.

			17 is in the list since 17 = 23 - (2*3).

Cf. A157677, A225303, A225319.

Union[Select[Table[p=Prime[n]; p-Times@@IntegerDigits[p],{n,150}],PrimeQ]]

cp's OEIS Frontend

A227217 Primes p such that p + (product of digits of p) is prime and p - (product of digits of p) is prime.

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A229176 Primes p with nonzero digits such that p + product_of_digits and p - product_of_digits are both prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

A225677 Primes of the form p - (product of digits of p), where p is a prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica