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 1-10 of 20 results. Next

A134809 Cyclops primes.

Original entry on oeis.org

101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 13033, 13037, 13043, 13049, 13063
Offset: 1

Views

Author

Omar E. Pol, Nov 25 2007

Keywords

Comments

Cyclops numbers that are prime numbers: primes with an odd number of digits with middle digit 0 that have only one digit 0.
The only known Fibonacci number in this sequence is 99194853094755497 (see A005478 and A182809).
The only known Lucas number in this sequence is 688846502588399 (see A005479 and A182811).

Links

Crossrefs

Intersection of prime numbers A000040 and cyclops numbers A134808.
Cf. A005478, A005479, A056709, A069675, A182809, A182811.

Programs

  • Mathematica
    (* First run the program given for A134808 *) Select[Prime[Range[2000]], cyclopsQ] (* Alonso del Arte, Dec 16 2010 *)
cycQ[n_]:=Module[{idn=IntegerDigits[n],len},len=Length[idn];OddQ[len] && Count[idn,0] == 1 && idn[[(len+1)/2]]==0]; Select[Flatten[Table[Prime[ Range[ PrimePi[10^(2n)+1],PrimePi[10^(2n+1)]]],{n,2}]],cycQ] (* Harvey P. Dale, Jun 20 2014 *)
  • Python
    # cyclops() in A134808
from sympy import isprime
print([c for c in cyclops(upto=13063) if isprime(c)]) # Michael S. Branicky, Jan 05 2021

Extensions

Links added by Omar E. Pol, Mar 25 2011

A069684 Primes with either no internal digits or all internal digits are 9.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 191, 193, 197, 199, 293, 397, 491, 499, 593, 599, 691, 797, 991, 997, 1993, 1997, 1999, 2999, 4993, 4999, 6991, 6997, 7993, 8999, 19991, 19993, 19997, 49991, 49993, 49999
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Links

Crossrefs

Cf. A069675, A069676, A069677, A069678, A069679, A069680, A069681, A069682, A069683.

Programs

  • Mathematica
    Join[Prime[Range[25]],Select[Flatten[Table[FromDigits[Join[{d1},PadRight[{},n,9],{d2}]],{n,150},{d1,9},{d2,{1,3,7,9}}]],PrimeQ]] (* Harvey P. Dale, Nov 10 2024 *)
Join[Prime[Range[25]],Select[Prime[Range[26,5200]],Union[Most[Rest[IntegerDigits[#]]]]=={9}&]] (* Harvey P. Dale, Jul 29 2025 *)

Extensions

Corrected by Ray Chandler, Nov 24 2003
Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011

A069676 Primes with either no internal digits or all internal digits are 1.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 211, 311, 313, 317, 419, 613, 617, 619, 719, 811, 911, 919, 1117, 2111, 2113, 3119, 4111, 5113, 5119, 6113, 8111, 8117, 11113, 11117, 11119, 41113, 41117, 71119
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Links

Crossrefs

Cf. A069675, A069677, A069678, A069679, A069680, A069681, A069682, A069683, A069684.

Programs

  • Mathematica
    aid1Q[n_]:=Union[Most[Rest[IntegerDigits[n]]]]=={1}; Join[Prime[Range[PrimePi[ 100]]], Select[Prime[Range[PrimePi[100]+1,7100]],aid1Q]] (* Harvey P. Dale, Apr 12 2013 *)
  • PARI
    lista(na) = my(vp = List(primes(primepi(100)))); for (n=1, na, my(x=(10^n-1)/9); for (i=1, 9, forstep(j=1, 9, 2, my(y=10^(n+1)*i + 10*x + j); if (ispseudoprime(y), listput(vp, y));););); Vec(vp); \\ Michel Marcus, Jul 12 2022

Extensions

Corrected by Ray Chandler, Nov 24 2003
Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011

A069677 Primes with either no internal digits or all internal digits are 2.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 127, 223, 227, 229, 421, 521, 523, 727, 821, 823, 827, 829, 929, 1223, 1229, 2221, 3221, 3229, 4229, 5227, 6221, 6229, 7229, 8221, 9221, 9227, 12227, 22229, 42221
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Links

Crossrefs

Cf. A069675, A069676, A069678, A069679, A069680, A069681, A069682, A069683, A069684.

Programs

  • Mathematica
    Join[Prime[Range[25]],Select[Prime[Range[26,4500]],Union[Most[ Rest[ IntegerDigits[ #]]]] =={2}&]] (* Harvey P. Dale, Aug 12 2021 *)
  • PARI
    uptoqdigits(n) = { my(ld = [1,3,7,9]); n = max(n, 2); res = List(primes(primepi(97))); for(i = 1, n-2, twos = 20*(10^i\9); for(j = 1, 9, for(k = 1, #ld, c = j*10^(i+1) + twos + ld[k]; if(isprime(c), listput(res, c) ) ) ) ); Set(res) } \\ David A. Corneth, Aug 12 2021
  • Python
    from sympy import isprime
def agen(maxdigits):
    yield from [2, 3, 5, 7]
    for d in range(2, maxdigits+1):
        pow10, mid = 10**(d-1), 0 if d < 3 else 10*int('2'*(d-2))
        cands = (a*pow10+mid+b for a in range(1, 10) for b in [1, 3, 7, 9])
        yield from filter(isprime, cands)
print([an for an in agen(100)]) # Michael S. Branicky, Aug 12 2021

Extensions

Corrected by Ray Chandler, Nov 24 2003
Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011

A069678 Primes with either no internal digits or all internal digits are 3.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 131, 137, 139, 233, 239, 331, 337, 431, 433, 439, 631, 733, 739, 839, 937, 2333, 2339, 3331, 4337, 4339, 5333, 6337, 7331, 7333, 9337, 13331, 13337, 13339, 23333, 23339
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Links

Crossrefs

Cf. A069675, A069676, A069677, A069679, A069680, A069681, A069682, A069683, A069684.

Programs

  • Mathematica
    Join[Prime[Range[25]],Select[Flatten[Table[10FromDigits[PadRight[{n},k,3]]+d,{n,9},{d,{1,3,7,9}},{k,2,5}]],PrimeQ]]//Sort (* Harvey P. Dale, Aug 08 2020 *)

Extensions

Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011

A069679 Primes with either no internal digits or all internal digits are 4.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 149, 241, 347, 349, 443, 449, 541, 547, 641, 643, 647, 743, 941, 947, 1447, 2441, 2447, 3449, 4441, 4447, 5441, 5443, 5449, 6449, 8443, 8447, 14447, 14449, 24443, 44449
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Links

Crossrefs

Cf. A069675, A069676, A069677, A069678, A069680, A069681, A069682, A069683, A069684.

Programs

  • Mathematica
    Join[Prime[Range[25]],Select[Prime[Range[26,5000]],Union[Most[Rest[ IntegerDigits[ #]]]] =={4}&]] (* Harvey P. Dale, Dec 08 2022 *)

Extensions

Corrected by Ray Chandler, Nov 24 2003
Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011

A069680 Primes with either no internal digits or all internal digits are 5.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 151, 157, 251, 257, 353, 359, 457, 557, 653, 659, 751, 757, 853, 857, 859, 953, 1553, 1559, 2551, 2557, 3557, 3559, 5557, 6551, 6553, 7559, 9551, 15551, 15559, 45553
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Crossrefs

Cf. A069675, A069676, A069677, A069678, A069679, A069681, A069682, A069683, A069684.

Extensions

Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011

A069681 Primes with either no internal digits or all internal digits are 6.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 163, 167, 263, 269, 367, 461, 463, 467, 563, 569, 661, 761, 769, 863, 967, 1663, 1667, 1669, 2663, 4663, 5669, 6661, 7669, 8663, 8669, 9661, 16661, 26669, 46663, 56663
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Crossrefs

Cf. A069675, A069676, A069677, A069678, A069679, A069680, A069682, A069683, A069684.

Extensions

Corrected by Ray Chandler, Nov 24 2003
Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011

A069682 Primes with either no internal digits or all internal digits are 7.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 173, 179, 271, 277, 373, 379, 479, 571, 577, 673, 677, 773, 877, 971, 977, 1777, 2777, 3779, 5779, 6779, 8779, 27773, 27779, 47777, 47779, 57773, 67777, 77773, 97771
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Crossrefs

Cf. A069675, A069676, A069677, A069678, A069679, A069680, A069681, A069683, A069684.

Extensions

Corrected by Ray Chandler, Nov 24 2003
Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011

A069683 Primes with either no internal digits or all internal digits are 8.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 181, 281, 283, 383, 389, 487, 587, 683, 787, 881, 883, 887, 983, 1889, 2887, 3881, 3889, 4889, 5881, 6883, 7883, 8887, 9883, 9887, 48883, 48889, 58889, 68881, 78887
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Crossrefs

Cf. A069675, A069676, A069677, A069678, A069679, A069680, A069681, A069682, A069684.

Extensions

Corrected by Ray Chandler, Nov 24 2003
Offset corrected and name changed by Arkadiusz Wesolowski, Sep 07 2011
Showing 1-10 of 20 results. Next

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