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 25 results. Next

A082720 Digit lengths for which there exist plateau or depression primes of the general form a*(10^m-1)/9 +- b*(10^(m-1)+1).

Original entry on oeis.org

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33, 37, 41, 49, 53, 55, 59, 61, 65, 67, 69, 73, 75, 83, 85, 87, 93, 95, 97, 101, 103, 105, 111, 113, 115, 117, 121, 127, 129, 141, 157, 161, 171, 193, 201, 205, 209, 231, 247, 291, 323, 343, 351, 353, 361, 367, 401
Offset: 0

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Crossrefs

Cf. A082697-A082719, A077797, A077799.

A068645 Primes in which a string of 3's is sandwiched between two 1's.

Original entry on oeis.org

11, 131, 13331, 1333331, 13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
Offset: 1

Views

Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

a(5) consists of 93 and a(6) consists of 159 3's sandwiched between two 1's. - Sascha Kurz, Mar 26 2002
a(8) has 1471 digits. - Michael S. Branicky, Jan 27 2023

Links

Crossrefs

Cf. A056244, A082697.

Programs

  • Mathematica
     Select[Flatten[Table[10*FromDigits[PadRight[{1},n,3]]+1,{n,120}]],PrimeQ] (* Harvey P. Dale, Aug 09 2020 *)
  • Python
    from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(0) if isprime(t:=int("1" + "3"*i + "1")))
print(list(islice(agen(), 7))) # Michael S. Branicky, Jan 27 2023

Extensions

More terms from Sascha Kurz, Mar 26 2002
Edited by Ray Chandler, Nov 04 2014

A082700 Numbers k such that (15*10^(k-1) - 51)/9 is a plateau prime.

Original entry on oeis.org

5, 13, 17, 19, 37, 53, 73, 101, 6233, 24029, 40223, 66395
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.

Examples

			k=13 -> (15*10^(13-1) - 51)/9 = 1666666666661.

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Crossrefs

Cf. A056247, A068647, A082697-A082720.

Programs

  • PARI
    is(n)=ispseudoprime(2*(10^n-1)/3-5*(10^(n-1)+1)) || ispseudoprime(15*10^(n-1)-51)/9 \\ Charles R Greathouse IV, Feb 07 2013

Formula

a(n) = A056247(n+1) + 2.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Edited by Ray Chandler, Nov 04 2014

A082703 Numbers k such that (18*10^(k-1) - 81)/9 is a plateau prime.

Original entry on oeis.org

3, 5, 9, 41, 87, 201, 731, 1461, 23673, 28631
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.

Examples

			k=9 -> (18*10^(9-1) - 81)/9 = 199999991.

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Crossrefs

Cf. A082697-A082720, A056250, A068649.

Formula

a(n) = A056250(n+1) + 2.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Edited by Ray Chandler, Nov 04 2014

A082719 Numbers k such that (89*10^(k-1) + 1)/9 is a depression prime.

Original entry on oeis.org

7, 73, 97, 115, 205, 985, 1227, 4795, 20721, 133581, 411591
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No other terms below 700000. - Serge Batalov, Sep 22 2014

Examples

			k=7 -> (89*10^(7-1) + 1)/9 = 8*(10^7 - 1)/9 + (10^6 + 1) = 8888888 + 1000001 = 9888889.

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Crossrefs

Cf. A082697-A082719, A056266.

Extensions

Additional PRP term 133581 from Serge Batalov, May 15 2010
Additional PRP term 411591 from Serge Batalov, Sep 22 2014
Edited by Ray Chandler, Nov 05 2014
Definition revised by N. J. A. Sloane, Oct 30 2019

A056244 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 21 for n > 0.

Original entry on oeis.org

0, 1, 3, 5, 93, 159, 359, 1469, 2897, 3093, 3111, 15697, 17955, 42261, 111031
Offset: 1

Views

Author

Robert G. Wilson v, Aug 18 2000

Keywords

Comments

Numbers n such that (120*10^n - 21)/9 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 3 followed by digit 1 is prime.
Numbers corresponding to terms <= 3111 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

Examples

			131 is prime, hence 1 is a term.

References

  • Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

Crossrefs

Cf. A000533, A002275, A068645, A082697.

Programs

  • Mathematica
    Do[If[PrimeQ[(1*10^n + 3*(10^n - 1)/9)*10 + 1], Print[n]], {n, 1, 2500}]
Select[Range[0, 2000], PrimeQ[(120 10^# - 21) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
  • PARI
    a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+21)
  • PARI
    for(n=0,1500,if(isprime((120*10^n-21)/9),print1(n,",")))

Formula

a(n) = A082697(n-1) - 2 for n > 1.

Extensions

More terms and additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
Edited by N. J. A. Sloane, Jun 15 2007
Updates from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(15)=111031 from Ray Chandler, Apr 14 2011
Updated comments section and a link, by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 04 2014

A082698 Numbers k such that (13*10^(k-1) - 31)/9 is a plateau prime.

Original entry on oeis.org

7, 67, 1255, 8407, 67039
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
a(6) > 2*10^5. - Tyler Busby, Feb 02 2023

Examples

			k=7 -> (13*10^(7-1) - 31)/9 = 1444441.

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Crossrefs

Cf. A056245, A082697-A082720.

Formula

a(n) = A056245(n+1) + 2.

Extensions

A new PRP term from Serge Batalov, Nov 02 2008
Edited by Ray Chandler, Nov 04 2014

A082699 Numbers k such that (14*10^(k-1) - 41)/9 is a plateau prime.

Original entry on oeis.org

3, 5, 21, 33, 401, 563, 7017, 37685
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.

Examples

			k=21 -> (14*10^(21-1) - 41)/9 = 155555555555555555551.

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Crossrefs

Cf. A056246, A068646, A082697-A082720.

Formula

a(n) = A056246(n+1) + 2.

Extensions

37685 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Edited by Ray Chandler, Nov 04 2014

A082702 Numbers k such that (17*10^(k-1) - 71)/9 is a plateau prime.

Original entry on oeis.org

3, 9, 15, 41, 93, 129, 885, 9425, 14769, 19259, 31235
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.

Examples

			k=15 -> (17*10^(15-1) - 71)/9 = 188888888888881.

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Crossrefs

Cf. A082697-A082720, A056249.

Formula

a(n) = A056249(n+1) + 2.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Edited by Ray Chandler, Nov 04 2014

A082704 Numbers k such that (28*10^(k-1) + 17)/9 is a depression prime.

Original entry on oeis.org

3, 13, 15, 31, 105, 127, 343, 601, 9825
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
a(10) > 2^16. - Lucas A. Brown, Apr 18 2021
a(10) > 2*10^5. - Tyler Busby, Feb 01 2023

Examples

			k=15 -> (28*10^(15-1) + 17)/9 = 311111111111113.

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Crossrefs

Cf. A082697-A082720, A056251, A068650.

Formula

a(n) = A056251(n) + 2.

Extensions

Edited by Ray Chandler, Nov 04 2014
Showing 1-10 of 25 results. Next

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