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 28 results. Next

A062232 Numbers k such that the smoothly undulating palindromic number (98*10^k - 89)/99 is a prime.

Original entry on oeis.org

9, 161, 219, 4859, 21989, 52931, 88595
Offset: 1

Views

Author

Patrick De Geest and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=9 -> (98*10^9 - 89)/99 = 989898989.

Links

Crossrefs

Cf. A062209-A062231, A059758, A032758.

Extensions

a(6)=52931 from Ray Chandler, Nov 11 2010
a(7)=88595 from Ray Chandler, Jul 23 2011
Edited by Ray Chandler, Aug 17 2011

A037487 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,2.

Original entry on oeis.org

1, 12, 121, 1212, 12121, 121212, 1212121, 12121212, 121212121, 1212121212, 12121212121, 121212121212, 1212121212121, 12121212121212, 121212121212121, 1212121212121212, 12121212121212121, 121212121212121212, 1212121212121212121, 12121212121212121212
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

See A037610 for a general formula. - Hieronymus Fischer, Jan 03 2013
(Smoothly undulating palindromic) primes in this sequence are listed in A092696(n) = (4*10^A062209(n)-7)/33. - M. F. Hasler, Jul 30 2015

Links

Crossrefs

Cf. A037610.

Programs

  • Mathematica
    Table[FromDigits[PadRight[{},n,{1,2}]],{n,20}] (* or *) LinearRecurrence[ {10,1,-10},{1,12,121},20] (* Harvey P. Dale, Jun 21 2016 *)
  • PARI
    A037487(n)=10^n*4\33  \\ - M. F. Hasler, Jan 13 2013
  • PARI
    Vec(x*(2*x+1)/((x-1)*(x+1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Apr 30 2014

Formula

a(n) = floor((4/33)*10^n). - Hieronymus Fischer, Jan 03 2013
a(n) = 10*a(n-1)+a(n-2)-10*a(n-3). G.f.: x*(2*x+1) / ((x-1)*(x+1)*(10*x-1)). - Colin Barker, Apr 30 2014

A092696 Smoothly undulating palindromic primes of the form (12*10^n-21)/99.

Original entry on oeis.org

1212121, 12121212121, 1212121212121212121212121212121212121212121
Offset: 1

Views

Author

Rick L. Shepherd, Mar 04 2004

Keywords

Comments

The De Geest link calls these smoothly undulating palindromic primes. Corresponding n are given in A062209. Equivalently, primes of the form 1212...121: Decimal digits "12" repeated k times with 1 appended (or "21" repeated k times with 1 prefixed). Corresponding k are given in A056803. The next term, a(4), has "12" repeating A056803(4) = 69 times and length A062209(4) = 2*A056803(4) + 1 = 139 decimal digits.

Links

Crossrefs

Cf. A056803 (number of 12's (or 21's)), A062209 (corresponding decimal digit lengths).
Cf. A032758, A033619, A030291, A059168, A242541, A004022.

Formula

a(n) = (4*10^A062209(n)-7)/33. - M. F. Hasler, Jul 30 2015

Extensions

Edited by M. F. Hasler, Jul 30 2015

A056803 Numbers k such that k copies of 12 followed by 1 is a palindromic prime.

Original entry on oeis.org

3, 5, 21, 69, 313, 699, 798, 989, 3904, 7029, 23249
Offset: 1

Views

Author

Robert G. Wilson v, Aug 22 2000

Keywords

Examples

			12121212121 is prime so 5 is a term.

Links

Crossrefs

Corresponding primes are given in A092696. Corresponding decimal digit lengths are given in A062209. a(k) = (A062209(k-1)-1)/2.

Programs

  • Mathematica
    Do[m = n; If[PrimeQ[120(10^(2n) - 1)/99 + 1], Print[n]], {n, 1, 600}]
(IntegerLength[#]-1)/2&/@Select[10#+1&/@Table[FromDigits[Flatten[ IntegerDigits/@ PadRight[{},n,{1,2}]]],{n,2,15000,2}],PrimeQ] (* Harvey P. Dale, Apr 02 2020 *)

Extensions

More terms from Rick L. Shepherd, Mar 04 2004
Definition clarified by N. J. A. Sloane, Nov 09 2024
a(11) from Michael S. Branicky, Dec 11 2024

A077799 Numbers m such that a smoothly undulating palindromic prime of the form (rs*10^m-sr)/99 exists, where r and s are two distinct digits and rs and sr denote concatenations of those digits.

Original entry on oeis.org

3, 5, 7, 9, 11, 15, 17, 21, 23, 25, 27, 31, 33, 37, 39, 43, 45, 51, 55, 57, 63, 65, 71, 77, 81, 83, 89, 95, 99, 109, 133, 139, 143, 145, 149, 161, 163, 195, 209, 219, 225, 229, 237, 243, 245, 277, 315, 357, 479, 513, 515, 537, 551, 561, 567, 583, 627, 849, 857
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

Edited by Ray Chandler, Aug 17 2011
Name clarified by Sean A. Irvine, Jun 14 2025

A062210 Numbers k such that the smoothly undulating palindromic number (14*10^k - 41)/99 is a prime.

Original entry on oeis.org

11, 277, 479, 583, 1631, 6343, 14689
Offset: 1

Views

Author

Patrick De Geest and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			11 is in the sequence because (14*10^11 - 41)/99 = 14141414141 is prime.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

Edited by Ray Chandler, Aug 17 2011
Name and Example edited by Jon E. Schoenfield, Jun 25 2017

A062216 Numbers k such that the smoothly undulating palindromic number (31*10^k - 13)/99 is a prime.

Original entry on oeis.org

3, 51, 83, 225, 561, 10419, 18255, 43869
Offset: 1

Views

Author

Patrick De Geest and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=51 -> (31*10^51 - 13)/99 = 313131313131313131313131313131313131313131313131313.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

43869 from Ray Chandler, Sep 30 2010
Edited by Ray Chandler, Aug 17 2011

A062220 Numbers k such that the smoothly undulating palindromic number (38*10^k - 83)/99 is a prime.

Original entry on oeis.org

3, 9, 15, 17, 21, 57, 4233, 4335, 13221, 26447, 29897, 91997
Offset: 1

Views

Author

Patrick De Geest and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=21 -> (38*10^21 - 83)/99 = 383838383838383838383.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

a(12)=91997 from Ray Chandler, Jul 29 2011
Edited by Ray Chandler, Aug 17 2011

A062231 Numbers k such that the smoothly undulating palindromic number (97*10^k - 79)/99 is a prime.

Original entry on oeis.org

9, 27, 45, 237
Offset: 1

Views

Author

Patrick De Geest and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=27 -> (97*10^27 - 79)/99 = 979797979797979797979797979.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Programs

  • Mathematica
    Select[Range[1,239,2],PrimeQ[FromDigits[PadRight[{},#,{9,7}]]]&] (* Harvey P. Dale, Mar 24 2021 *)

Extensions

Edited by Ray Chandler, Aug 17 2011

A062211 Numbers k such that the smoothly undulating palindromic number (15*10^k - 51)/99 is a prime.

Original entry on oeis.org

3, 15, 63, 89, 245, 583, 1791, 2123, 7233, 24787, 44653
Offset: 1

Views

Author

Patrick De Geest and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
No further terms < 100000. - Ray Chandler, Aug 17 2011

Examples

			k=15 -> (15*10^15 - 51)/99 = 151515151515151.

Links

Crossrefs

Cf. A062209-A062232, A059758, A032758.

Extensions

a(11)=44653 from Ray Chandler, Nov 11 2010
Edited by Ray Chandler, Aug 17 2011
Showing 1-10 of 28 results. Next

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