A107612 -id:A107612 - cp's OEIS frontend

A081982 Primes p such that p+1 is divisible by the digital product (of nonzero digits) of p.

11, 23, 101, 113, 131, 167, 211, 233, 311, 431, 863, 1013, 1021, 1031, 1061, 1103, 1201, 1217, 1223, 1259, 1301, 1601, 1619, 1637, 1721, 1823, 2003, 2011, 2111, 2687, 3011, 3023, 3203, 4111, 4703, 6011, 6047, 6101, 6173, 6263, 6911, 7013

Offset: 1

Amarnath Murthy, Apr 04 2003

Contains A020449 and A107612 (except 2). - Robert Israel, Nov 09 2017

			167 is a term as 168 is divisible by 1*6*7 = 42.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A020449, A081981, A081983, A081984, A081986, A081987, A107612, A101987.

filter:= proc(n)
isprime(n) and
n+1 mod convert(subs(0=NULL,convert(n,base,10)),`*`) = 0
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Nov 09 2017

isok(p) = isprime(p) && (d=digits(p)) && !((p+1) % prod(k=1, #d, if (d[k], d[k], 1))); \\ Michel Marcus, Nov 09 2017

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

A107611 Indices of primes with digit product = 2.

Original entry on oeis.org

1, 47, 318, 10546, 10552, 10629, 86544, 56196114, 56200915, 56676030, 4555804158, 4559732893, 77220966866, 2907021742443997, 2907021767925176, 2907024290266584, 2932496986613869, 51280189662853652, 2461813897281353935, 23422580231698333926, 23422580438055032295

Offset: 1

Zak Seidov, May 17 2005

Next term is A000720(111111111111112111) > A000720(10^17) > 2*10^15.

Kim Walisch, Fast C++ prime counting function implementation (primecount).

Corresponding primes in A107612.

Cf. A000720, A053666, A101987, A107612.

Do[If[Apply[Times, IntegerDigits[Prime[n]]]==2, Print[n]], {n, 100000}]

a(n) = A000720(A107612(n)). - David Wasserman, May 07 2008

More terms from Ryan Propper, Jan 03 2008

a(14)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Sep 03 2024

A199980 Primes whose multiplicative digital root is 2.

Original entry on oeis.org

2, 37, 43, 73, 137, 173, 211, 223, 317, 367, 389, 431, 673, 827, 839, 929, 983, 1223, 1279, 1297, 1367, 1447, 1621, 1637, 1693, 1999, 2111, 2161, 2179, 2213, 2269, 2339, 2393, 2663, 2699, 2719, 2791, 2917, 2969, 2971, 3167, 3169, 3221, 3329, 3463, 3499, 3617

Offset: 1

Jaroslav Krizek, Nov 13 2011

Complement of A199981 with respect to A034049, numbers whose multiplicative digital root is 2.

			Prime 389 is in sequence because 3*8*9=216, 2*1*6 =12, 1*2=2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A199981 (nonprime numbers whose multiplicative digital root is 2).
Includes A107612.
Cf. A031347, A034049.

mdr:= proc(n) option remember;
  local t;
  t:= convert(convert(n,base,10),`*`);
  if t < 10  then t else procname(t) fi
end proc:
select(t -> mdr(t) = 2 and isprime(t), [2, seq(i,i=3..10000,2)]); # Robert Israel, Nov 05 2020

t = {}; n = 0; While[Length[t] < 100, n = NextPrime[n]; s = n; While[s >= 10, s = Times @@ IntegerDigits[s]]; If[s == 2, AppendTo[t, n]]]; t (* T. D. Noe, Nov 15 2011 *)
Select[Prime[Range[600]],FixedPoint[Times@@IntegerDigits[#]&,#]==2&] (* Harvey P. Dale, Mar 28 2012 *)

A135048 Indices of primes with digit product = 3.

Original entry on oeis.org

2, 6, 11, 30, 32, 64, 1346, 1349, 1367, 10715, 12253, 26886, 733412, 733420, 733533, 734596, 6363182, 6363183, 6363289, 7437658, 503193257, 503193259, 503279746, 504057767, 1346029458, 4555878955, 12238593622, 1035905650780, 309353882444942, 2907021742443975

Offset: 1

Zak Seidov, Feb 11 2008

The corresponding primes are in A107689.

Amiram Eldar, Table of n, a(n) for n = 1..37 (calculated using Kim Walisch's primecount)
Kim Walisch, Fast C++ prime counting function implementation (primecount).

Cf. A107611, A107612, A107689.

a(n) = primepi(A107689(n)).

a(26)-a(30) from Amiram Eldar, Sep 06 2024

A201015 Composite numbers whose product of digits is 2.

Original entry on oeis.org

12, 21, 112, 121, 1112, 1121, 1211, 11112, 11121, 11211, 12111, 21111, 111112, 121111, 211111, 1111112, 1111121, 1112111, 1121111, 1211111, 2111111, 11111112, 11111121, 11111211, 11112111, 11121111, 11211111, 12111111, 21111111, 111111112, 111111121, 111111211

Offset: 1

Jaroslav Krizek, Nov 25 2011

Complement of A107612 with respect to A199986. Subsequence of A199981 (composite numbers whose multiplicative digital root is 2).

			Number 121 is in sequence because 1*2*1 = 2, and 121 = 11*11 is composite.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A107612 (primes whose product of digits is 2), A199986 (numbers whose product of digits is 2).

Select[Sort[Flatten[Table[FromDigits/@Permutations[PadRight[{2},n,1]],{n,2,9}]]],CompositeQ] (* Harvey P. Dale, Oct 06 2024 *)

from sympy import isprime
def agen(maxdigits):
    for digs in range(1, maxdigits+1):
        for i in range(digs):
            t = int("1"*(digs-1-i) + "2" + "1"*i)
            if not isprime(t): yield t
print(list(agen(9))) # Michael S. Branicky, Dec 21 2021

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A081982 Primes p such that p+1 is divisible by the digital product (of nonzero digits) of p.

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A107611 Indices of primes with digit product = 2.

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A199980 Primes whose multiplicative digital root is 2.

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A135048 Indices of primes with digit product = 3.

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A201015 Composite numbers whose product of digits is 2.

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