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.

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A106116 Primes without {0, 1} as digits.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 223, 227, 229, 233, 239, 257, 263, 269, 277, 283, 293, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 433, 439, 443, 449, 457, 463, 467, 479, 487, 499, 523, 547, 557, 563, 569, 577, 587, 593
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Links

Crossrefs

Intersection of A038603 and A038618.
Cf. A000040, A106745.

Programs

  • Mathematica
    Select[Prime[Range[100]], Min[IntegerDigits[ # ]]>1&]
  • PARI
    is(p)=vecsort(digits(p),,8)[1]>1 && isprime(p) \\ Charles R Greathouse IV, Jan 02 2013

Formula

a(n) >> n^k with k = log 10/log 8 = 1.107.... - Charles R Greathouse IV, Jan 02 2013

Extensions

Terms > 523 added by Jonathan Vos Post, Feb 10 2010

A178558 Primes with exactly nine 9's.

Original entry on oeis.org

9199999999, 9299999999, 9959999999, 9995999999, 9999499999, 9999929999, 9999959999, 9999999929, 10999999999, 16999999999, 19399999999, 19909999999, 19991999999, 19999399999, 19999990999, 19999997999, 19999999199
Offset: 1

Views

Author

Lekraj Beedassy, May 29 2010

Keywords

Crossrefs

Cf. A038618, A178550-A178557

A178557 Primes with exactly eight 8's.

Original entry on oeis.org

888888883, 888888887, 8488888883, 8688888889, 8838888881, 8868888887, 8880888883, 8885888881, 8886888889, 8888088889, 8888488883, 8888808881, 8888818889, 8888838887, 8888848889, 8888868881, 8888868889, 8888880881
Offset: 1

Views

Author

Lekraj Beedassy, May 29 2010

Keywords

Crossrefs

Cf. A038618, A178550-6, A178558

A069490 Primes > 1000 in which every substring of lengths 2 and 3 are also prime.

Original entry on oeis.org

1373, 3137, 3797, 6131, 6173, 6197, 9719, 11311, 11317, 17971, 31379, 61379, 71971, 113131, 113173, 113797, 131311, 131317, 131797, 179719, 317971, 431311, 431797, 617971, 1131131, 1131379, 1311311, 1313797, 1317971, 3131137, 3131311
Offset: 1

Views

Author

Amarnath Murthy, Mar 30 2002

Keywords

Comments

For all terms: substrings of length 3 correspond to one of the first 21 terms of A069489. - Reinhard Zumkeller, Jun 08 2015

Examples

			11317 is a term as the substrings of length 2, i.e., 11, 13, 31, 17 and the three substrings of length 3, i.e., 113, 131 and 317 are all prime.

Links

Crossrefs

Cf. A069488 and A069489.
Cf. A010051, A038618.

Programs

  • Haskell
    import Data.Set (fromList, deleteFindMin, union)
a069490 n = a069490_list !! (n-1)
a069490_list = f $ fromList [1..9] where
   f s | m < 1000               = f s''
       | h m && a010051' m == 1 = m : f s''
       | otherwise              = f s''
       where s'' = union s' $ fromList $ map (+ (m * 10)) [1, 3, 7, 9]
             (m, s') = deleteFindMin s
   h x = x < 100 && a010051' x == 1 ||
         a010051' (x `mod` 1000) == 1 &&
         a010051' (x `mod` 100) == 1 && h (x `div` 10)
-- Reinhard Zumkeller, Jun 08 2015
  • Mathematica
    Do[ If[ Union[ PrimeQ[ Map[ FromDigits, Partition[ IntegerDigits[ Prime[n]], 2, 1]]]] == Union[ PrimeQ[ Map[ FromDigits, Partition[ IntegerDigits[ Prime[n]], 3, 1]]]] == {True}, Print[ Prime[n]]], {n, PrimePi[1000] + 1, 10^5}]
 Select[Prime[Range[169,226000]],AllTrue[FromDigits/@Flatten[Table[ Partition[ IntegerDigits[ #],k,1],{k,{2,3}}],1],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 02 2021 *)

Extensions

Edited, corrected and extended by Robert G. Wilson v, Apr 12 2002

A178551 Primes with exactly two 2's.

Original entry on oeis.org

223, 227, 229, 1223, 1229, 2027, 2029, 2129, 2203, 2207, 2213, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2423, 2521, 2621, 2729, 2927, 3221, 3229, 4229, 5227, 6221, 6229, 7229, 8221, 9221, 9227, 10223, 12203, 12211, 12239, 12241, 12251, 12253
Offset: 1

Views

Author

Lekraj Beedassy, May 29 2010

Keywords

Links

Crossrefs

Cf. A038618, A178550, A178552, A178553, A178554, A178555, A178556, A178557, A178558.

Programs

  • Mathematica
    Select[Prime[Range[1500]],Count[IntegerDigits[#],2]==2 &] (* Stefano Spezia, Aug 29 2025 *)
  • Python
    from sympy import isprime
print([i for i in range(10000) if str(i).count('2') == 2 and isprime(i)]) # Daniel Starodubtsev, Mar 29 2020

A178552 Primes with exactly three 3's.

Original entry on oeis.org

2333, 3313, 3323, 3331, 3343, 3373, 3433, 3533, 3733, 3833, 5333, 7333, 10333, 13033, 13313, 13331, 13337, 13339, 13633, 13933, 16333, 17333, 19333, 20333, 23339, 23633, 23833, 29333, 30133, 30313, 30323, 31033, 31337, 31393, 32233, 32303, 32323, 32353, 32363, 32533
Offset: 1

Views

Author

Lekraj Beedassy, May 29 2010

Keywords

Links

Crossrefs

Cf. A038618, A178550, A178551, A178553-A178558.

Programs

  • Mathematica
    Select[Prime[Range[3500]],Count[IntegerDigits[#],3]==3 &] (* Stefano Spezia, Aug 29 2025 *)

Extensions

Missing a(26) = 23633 and a(27) = 23833 inserted by Daniel Starodubtsev, Mar 14 2020

A178553 Primes with exactly four 4's.

Original entry on oeis.org

44449, 404449, 440441, 440443, 441443, 441449, 442447, 444043, 444047, 444341, 444343, 444347, 444349, 444401, 444403, 444421, 444461, 444463, 444469, 444473, 444487, 444547, 444641, 444649, 444841, 445447, 446441, 446447, 447443, 447449, 449441
Offset: 1

Views

Author

Lekraj Beedassy, May 29 2010

Keywords

Links

Crossrefs

Cf. A038618, A178550, A178551, A178552, A178554, A178555, A178556, A178557, A178558.

Programs

  • PARI
    isok(p) = isprime(p) && (#select(x->(x==4), digits(p)) == 4); \\ Michel Marcus, Mar 15 2020

Extensions

Missing a(13) = 444349 inserted by Daniel Starodubtsev, Mar 15 2020

A178554 Primes with exactly five 5's.

Original entry on oeis.org

555557, 1555553, 2555551, 3555551, 3555557, 4555559, 5055551, 5055559, 5355551, 5505551, 5535559, 5550553, 5550557, 5554553, 5555057, 5555059, 5555357, 5555507, 5555509, 5555527, 5555567, 5555591, 5555653, 5556557, 5556559, 5557553
Offset: 1

Views

Author

Lekraj Beedassy, May 29 2010

Keywords

Links

Crossrefs

Cf. A038618, A178550, A178551, A178552, A178553, A178555, A178556, A178557, A178558.

Programs

  • Mathematica
    Select[Prime[Range[PrimePi[55555],1000000]],Count[IntegerDigits[#],5]==5&]  (* Harvey P. Dale, Dec 20 2010 *)
  • PARI
    isok(p) = isprime(p) && (#select(x->(x==5), digits(p)) == 5); \\ Michel Marcus, Mar 15 2020

Extensions

Missing a(14) = 5554553 inserted by Daniel Starodubtsev, Mar 15 2020

A178555 Primes with exactly six 6's.

Original entry on oeis.org

16666669, 26666663, 26666669, 46666661, 46666663, 56666663, 60666667, 63666661, 64666661, 64666663, 64666669, 66066661, 66166663, 66466661, 66466667, 66466669, 66606667, 66616663, 66626663, 66646667, 66656663
Offset: 1

Views

Author

Lekraj Beedassy, May 29 2010

Keywords

Links

Crossrefs

Cf. A038618, A178550-A178554, A178556-A178558.

Programs

  • Maple
    f:= proc(m) local R, L, s, k, t,x;
  R:= NULL;
  for k from 9^(m-6) to 2*9^(m-6)-1 do
    t:= Vector(subs([8=9,7=8,6=7],convert(k,base,9)[1..m-6]));
    for s in combinat:-choose([$2..m],m-7) do
      L:= Vector(m,6);
      L[[1,op(s)]]:= t;
    if L[-1] = 0 then next fi;
      x:= add(L[i]*10^(i-1),i=1..m);
      if isprime(x) then R:= R, x fi;
  od od:
  op(sort([R]));
end proc:
f(8); # Robert Israel, May 08 2018

A178556 Primes with exactly seven 7's.

Original entry on oeis.org

77767777, 77777177, 77777377, 77777747, 137777777, 172777777, 177677777, 177776777, 177777377, 177777577, 177777727, 177777773, 177777779, 177797777, 197777777, 272777777, 277177777, 277727777, 277771777, 277775777, 277777177
Offset: 1

Views

Author

Lekraj Beedassy, May 29 2010

Keywords

Crossrefs

Cf. A038618, A178550-5, A178557-8

Programs

  • Mathematica
    Select[Prime[Range[45*10^5,152*10^5]],DigitCount[#,10,7]==7&] (* Harvey P. Dale, Dec 20 2022 *)
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