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 1-6 of 6 results.

A097223 Prime numbers p such that p = prime(n) and n = product of the digits of p.

Original entry on oeis.org

17, 73, 2475989
Offset: 1

Views

Author

Farideh Firoozbakht, Aug 06 2004

Keywords

Comments

This sequence is a subsequence of A097220, so the sequence is also a subsequence of A097221.
There is no further term. - Farideh Firoozbakht, Jul 15 2009

Examples

			2475989 is in the sequence because 2475989 is (2*4*7*5*9*8*9)-th prime.

Links

Crossrefs

Cf. A097220, A097221.

Programs

  • Mathematica
    v={}; Do[If[h=IntegerDigits[Prime[n]]; l=Length[h]; p=Product[h[[k]], {k, l}]; p==n, v=Append[v, Prime[n]]; Print[v]], {n, 205000000}]
  • PARI
    isok(p) = isprime(p) && (primepi(p) == vecprod(digits(p))); \\ Michel Marcus, Jan 27 2019

A097221 Numbers n such that for some k and a_1,a_2,...,a_k the concatenation of the a_i is equal to n and their product is equal to pi(n).

Original entry on oeis.org

16, 17, 63, 73, 132, 224, 322, 342, 352, 362, 364, 437, 545, 573, 619, 963, 1017, 1117, 1196, 1516, 2163, 2215, 2335, 2435, 2537, 3277, 3514, 3714, 4072, 4513, 4626, 5137, 6475, 8443, 11373, 11593, 11926, 12012, 12026, 12034, 12121, 12126, 12134, 12555
Offset: 1

Views

Author

Farideh Firoozbakht, Aug 05 2004

Keywords

Comments

A097220 is a subsequence of this sequence.

Examples

			90942236 is in the sequence because Pi(90942236)=909*42*23*6 in fact a1=909, a2=42, a3=23 & a4=6.

Crossrefs

Cf. A097220, A097222.

Programs

  • PARI
    composed(n,a)=my(d=0,k);if(a>=n,return(a==n));while(10^d0&a%k==0&composed(n\10^d,a/k),return(1)));0
isA097221(n)=composed(n,primepi(n))

Extensions

Corrected (2537,3277,4513,4626 were missing), extended, edited, and program added by Charles R Greathouse IV, Apr 23 2010

A097222 Numbers n such that for some k there exist k numbers a1,a2, ...,ak that concatenations of them is equal to n and sum of them is equal to Pi(n).

Original entry on oeis.org

15, 27, 39, 130, 131, 252, 370, 489, 1195, 2345, 3484, 4619, 5752, 6879
Offset: 1

Views

Author

Farideh Firoozbakht, Aug 05 2004

Keywords

Examples

			9642459 is in the sequence because Pi(9642459)=9+642459
in fact a1=9 & a2=642459.

Crossrefs

Cf. A097220, A097221.

A110070 Numbers n such that n=pi(d_1!*d_2!*...*d_k!) where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

0, 3, 34, 52, 2800414
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 22 2005

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Jul 21 2024

Examples

			2800414 is in the sequence because 2800414=pi(2!*8!*0!*0!*4!*1!*4!).

Crossrefs

Cf. A110071, A110072, A097220, A097223, A097227, A098683, A098684, A098685.

A117273 Numbers m such that the product of the digits of m is equal to the number of primes less than m.

Original entry on oeis.org

16, 53, 63, 364, 437, 545, 573, 829, 963, 5449, 6475, 23797, 67458, 2475998
Offset: 1

Views

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006

Keywords

Comments

This sequence is finite with its largest term < 10^70. - Stefan Steinerberger, Apr 24 2006
a(15) > 1.288 * 10^10 if it exists. - Kevin P. Thompson, Oct 19 2021

Examples

			364 is in the sequence because the product of its digits is 3*6*4 = 72 and there are 72 prime numbers smaller than 364.

Crossrefs

Cf. A000720, A007954, A097220.

Programs

  • Mathematica
    Select[Range[50000], DigitCount[ # ][[10]] == 0 && Product[i^DigitCount[ # ][[i]], {i, 1, 9}] == PrimePi[ # - 1] &] (* Stefan Steinerberger, Apr 24 2006 *)
g[n_] := Product[IntegerDigits[n][[m]], {m, 1, Length[IntegerDigits[n]]}]; Do[If[g[n] == PrimePi[n], Print[n]], {n, 1, 10000000}] (* Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006 *)
  • PARI
    isok(m) = vecprod(digits(m)) == primepi(m); \\ Michel Marcus, Oct 23 2021

Extensions

More terms from Zak Seidov, Stefan Steinerberger and Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006

A307851 Prime numbers prime(k) with a zeroless decimal representation such that (product of decimal digits of prime(k)) / k is an integer.

Original entry on oeis.org

2, 17, 73, 89, 2475989
Offset: 1

Views

Author

Ctibor O. Zizka, May 01 2019

Keywords

Examples

			For k = 21, prime(21) = 73, product of decimal digits of prime(k) / k = 7 * 3 / 21 = 1 so prime(21) = 73 is in the sequence.

Links

Crossrefs

Cf. A000040, A007954, A052382, A097220, A097223, A306766.

Programs

  • PARI
    lista(nn) = {my(ip=0, d); forprime(p=2, nn, ip++; d = digits(p); if (vecmin(d) && !(frac(vecprod(d)/ip)), print1(p, ", ")););} \\ Michel Marcus, May 02 2019
  • Python
    from math import prod
from sympy import nextprime
def aupton(terms):
  p, k, t = 2, 1, 0
  while t < terms:
    strp = str(p)
    if '0' not in strp and prod(int(d) for d in strp)%k == 0:
      t += 1; print(p, end=", ")
    p, k = nextprime(p), k+1
aupton(5) # Michael S. Branicky, Feb 17 2021

Extensions

a(5) from Alois P. Heinz, May 01 2019
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.