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 1-3 of 3 results.

A019546 Primes whose digits are primes; primes having only {2, 3, 5, 7} as digits.

Original entry on oeis.org

2, 3, 5, 7, 23, 37, 53, 73, 223, 227, 233, 257, 277, 337, 353, 373, 523, 557, 577, 727, 733, 757, 773, 2237, 2273, 2333, 2357, 2377, 2557, 2753, 2777, 3253, 3257, 3323, 3373, 3527, 3533, 3557, 3727, 3733, 5227, 5233, 5237, 5273, 5323, 5333, 5527, 5557
Offset: 1

Views

Author

R. Muller

Keywords

Comments

Intersection of A046034 and A000040; A055642(a(n)) = A193238(a(n)). - Reinhard Zumkeller, Jul 19 2011
Ribenboim mentioned in 2000 the following number as largest known term: 72323252323272325252 * (10^3120 - 1) / (10^20 - 1) + 1. It has 3120 digits, and was discovered by Harvey Dubner in 1992. Larger terms are 22557252272*R(15600)/R(10) and 2255737522*R(15600) where R(n) denotes the n-th repunit (see A002275): Both have 15600 digits and were found in 2002, also by Dubner (see Weisstein link). David Broadhurst reports in 2003 an even longer number with 82000 digits: (10^40950+1) * (10^20055+1) * (10^10374 + 1) * (10^4955 + 1) * (10^2507 + 1) * (10^1261 + 1) * (3*R(1898) + 555531001*10^940 - R(958)) + 1, see link. - Reinhard Zumkeller, Jan 13 2012
The smallest and largest primes that use exactly once the four prime decimal digits are respectively a(27)= 2357 and a(54) = 7523. - Bernard Schott, Apr 27 2023

References

  • Paulo Ribenboim, Prime Number Records (Chap 3), in 'My Numbers, My Friends', Springer-Verlag 2000 NY, page 76.

Links

Crossrefs

Cf. A045336, A003631, A034844, A179336, A109066, A215927.
Cf. A020463 (subsequence).
A093162, A093164, A093165, A093168, A093169, A093672, A093674, A093675, A093938 and A093941 are subsequences. - XU Pingya, Apr 20 2017

Programs

  • Haskell
    a019546 n = a019546_list !! (n-1)
a019546_list = filter (all (`elem` "2357") . show )
                      ([2,3,5] ++ (drop 2 a003631_list))
-- Or, much more efficient:
a019546_list = filter ((== 1) . a010051) $
                      [2,3,5,7] ++ h ["3","7"] where
   h xs = (map read xs') ++ h xs' where
     xs' = concat $ map (f xs) "2357"
     f xs d = map (d :) xs
-- Reinhard Zumkeller, Jul 19 2011
  • Magma
    [p: p in PrimesUpTo(5600) | Set(Intseq(p)) subset [2,3,5,7]]; // Bruno Berselli, Jan 13 2012
  • Mathematica
    Select[Prime[Range[700]], Complement[IntegerDigits[#], {2, 3, 5, 7}] == {} &] (* Alonso del Arte, Aug 27 2012 *)
Select[Prime[Range[700]], AllTrue[IntegerDigits[#], PrimeQ] &] (* Ivan N. Ianakiev, Jun 23 2018 *)
Select[Flatten[Table[FromDigits/@Tuples[{2,3,5,7},n],{n,4}]],PrimeQ] (* Harvey P. Dale, Apr 05 2025 *)
  • PARI
    is_A019546(n)=isprime(n) & !setminus(Set(Vec(Str(n))),Vec("2357")) \\ M. F. Hasler, Jan 13 2012
  • PARI
    print1(2); for(d=1,4, forstep(i=1,4^d-1,[1,1,2], p=sum(j=0,d-1,10^j*[2,3,5,7][(i>>(2*j))%4+1]); if(isprime(p), print1(", "p)))) \\ Charles R Greathouse IV, Apr 29 2015
  • Python
    from itertools import product
from sympy import isprime
A019546_list = [2,3,5,7]+[p for p in (int(''.join(d)+e) for l in range(1,5) for d in product('2357',repeat=l) for e in '37') if isprime(p)] # Chai Wah Wu, Jun 04 2021

Extensions

More terms from Cino Hilliard, Aug 06 2006
Thanks to Charles R Greathouse IV and T. D. Noe for massive editing support.

A056714 Numbers k such that 5*10^k + 3*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 1, 3, 13, 25, 49, 143, 419, 1705, 13993, 35753, 40889
Offset: 1

Views

Author

Robert G. Wilson v, Aug 11 2000

Keywords

Comments

Also numbers k such that (16*10^k - 1)/3 is prime.
5*10^a(n) + 3*(10^a(n) - 1)/9 is a solution for part (b) of questions of puzzle 244 from www.primepuzzles.net. If a(n) is greater than 5812 then a(n) is an example that is asked for in this question. - Farideh Firoozbakht, Dec 02 2003

Links

Crossrefs

Cf. A002275, A093674, A350995.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 5*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 5000}]

Extensions

1705 from Farideh Firoozbakht, Dec 18 2003
13993, 35753 and 40889 from Serge Batalov, Jan 2009 confirmed as next terms by Ray Chandler, Feb 11 2012

A276827 Primes p such that the greatest prime factor of 3*p+1 is at most 5.

Original entry on oeis.org

3, 5, 13, 53, 83, 853, 2083, 3413, 5333, 85333, 208333, 218453, 341333, 3495253, 5461333, 8533333, 13981013, 83333333, 853333333, 22369621333, 218453333333, 341333333333, 2236962133333, 3665038759253, 53333333333333, 91625968981333, 203450520833333, 1333333333333333
Offset: 1

Views

Author

Robert Israel, Sep 19 2016

Keywords

Comments

Prime(i) such that A087273(i) <= 5.

Links

Crossrefs

Cf. A087273.
Contains A093671, A093674, and A093676.

Programs

  • Maple
    N = 10^20: # to get all terms <= N
Res:= {}:
for a from 0 to ilog2(floor((3*N+1)/5)) do
  twoa:= 2^a;
  for b from (a mod 2) by 2 do
    p:= (twoa*5^b-1)/3;
    if p > N then break fi;
    if isprime(p) then
      Res:= Res union {p};
    fi
od od:
sort(convert(Res,list));
  • Mathematica
    Select[Prime@ Range[10^6], FactorInteger[3 # + 1][[-1, 1]] <= 5 &] (* Michael De Vlieger, Sep 19 2016 *)
  • PARI
    list(lim)=my(v=List(),s,t); lim=lim\1*3 + 1; for(i=0,logint(lim\2,5), t=if(i%2,2,4)*5^i; while(t<=lim, if(isprime(p=t\3), listput(v,p)); t<<=2)); Set(v) \\ Charles R Greathouse IV, Sep 19 2016
Showing 1-3 of 3 results.

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