cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A107612 Primes with digital product = 2.

Original entry on oeis.org

2, 211, 2111, 111121, 111211, 112111, 1111211, 1111111121, 1111211111, 1121111111, 111111211111, 111211111111, 2111111111111, 111111111111112111, 111111112111111111, 111111211111111111, 112111111111111111
Offset: 1

Views

Author

Zak Seidov, May 17 2005

Keywords

Comments

Corresponding indices of primes in A107611. Cf. A053666, A101987.

Links

Crossrefs

Cf. A053666, A101987, A107611.
Cf. A004022, A107689, A107690, A107691, A107692, A107693, A107694, A107695, A107696, A107697, A107698.

Programs

  • Maple
    for i from 0 to 30 do it:=sum(10^j, j=0..i): for k from 0 to i do if isprime(it+10^k) then printf(`%d,`, it+10^k) fi: od:od: (Sellers)
  • Mathematica
    Flatten[ Table[ Select[ Sort[ FromDigits /@ Permutations[ Flatten[{2, Table[1, {n}]}]]], PrimeQ[ # ] &], {n, 0, 19}]] (* Robert G. Wilson v, May 19 2005 *)
Select[Flatten[Table[FromDigits/@Permutations[PadRight[{2},n,1]],{n,20}]],PrimeQ]//Sort (* Harvey P. Dale, May 28 2017 *)

Formula

A107612(n) = prime(A107611(n)).

Extensions

More terms from Robert G. Wilson v and James Sellers, May 19 2005

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

Original entry on oeis.org

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

Views

Author

Amarnath Murthy, Apr 04 2003

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

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

Extensions

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

Views

Author

Zak Seidov, May 17 2005

Keywords

Comments

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

Links

Crossrefs

Corresponding primes in A107612.
Cf. A000720, A053666, A101987, A107612.

Programs

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

Formula

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

Extensions

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

A127482 Product of the nonzero digital products of all the prime numbers prime(1) to prime(n).

Original entry on oeis.org

2, 6, 30, 210, 210, 630, 4410, 39690, 238140, 4286520, 12859560, 270050760, 1080203040, 12962436480, 362948221440, 5444223321600, 244990049472000, 1469940296832000, 61737492466944000, 432162447268608000, 9075411392640768000, 571750917736368384000
Offset: 1

Views

Author

Alain Van Kerckhoven (alain(AT)avk.org), Sep 12 2007

Keywords

Examples

			a(7) = dp_10(2)*dp_10(3)*dp_10(5)*dp_10(7)*dp_10(11)*dp_10(13)*dp_10(17) = 2*3*5*7*(1*1)*(1*3)*(1*7) = 4410.

Links

Crossrefs

Cf. A000040, A007953, A007954, A051801, A101987, A131385, A131387, A131451.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<1, 1, a(n-1)*mul(
     `if`(i=0, 1, i), i=convert(ithprime(n), base, 10)))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Mar 11 2022
  • Mathematica
    Rest[FoldList[Times,1,Times@@Cases[IntegerDigits[#],Except[0]]&/@ Prime[ Range[ 20]]]] (* Harvey P. Dale, Mar 19 2013 *)
  • PARI
    f(n) = vecprod(select(x->(x>1), digits(prime(n)))); \\ A101987
a(n) = prod(k=1, n, f(k)); \\ Michel Marcus, Mar 11 2022
  • Python
    from math import prod
from sympy import sieve
def pod(s): return prod(int(d) for d in s if d != '0')
def a(n): return pod("".join(str(sieve[i+1]) for i in range(n)))
print([a(n) for n in range(1, 23)]) # Michael S. Branicky, Mar 11 2022

Formula

a(n) = Product_{k=1..n} dp_p(prime(k)) where prime(k)=A000040(k) and dp_p(m)=product of the nonzero digits of m in base p (p=10 for this sequence). - Hieronymus Fischer, Sep 29 2007
From Michel Marcus, Mar 11 2022: (Start)
a(n) = Product_{k=1..n} A051801(prime(k)).
a(n) = Product_{k=1..n} A101987(k). (End)

Extensions

Corrected and extended by Hieronymus Fischer, Sep 29 2007
Showing 1-4 of 4 results.

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