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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A077782 Numbers k such that (10^k - 1) - 5*10^floor(m/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

29, 45, 73, 209, 2273, 35729, 50897
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

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

Examples

			29 is a term because (10^29 - 1) - 5*10^14 = 99999999999999499999999999999.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[10^n - 5*10^Floor[n/2] - 1], Print[n]], {n, 3, 50900, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183185(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018

A077784 Numbers k such that (10^k - 1)/3 + 2*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 5, 35, 159, 237, 325, 355, 371, 481, 1649, 3641, 4709, 269623
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
a(13) > 2*10^5. - Robert Price, Apr 03 2016

Examples

			5 is a term because (10^5 - 1)/3 + 2*10^2 = 33533.

References

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

Links

Crossrefs

Partial sums of S(n, x), for x=1...9: A021823, A000217, A027941, A061278, A089817, A053142, A092521, A076765, A092420.
Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(10^n + 6*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 4800, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183175(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018
a(13) from Robert Price, Aug 03 2024

A077785 Odd numbers k such that the palindromic wing number (a.k.a. near-repdigit palindrome) 7*(10^k - 1)/9 - 2*10^((k-1)/2) is prime.

Original entry on oeis.org

3, 15, 27, 117, 259, 507, 3315, 4489, 4875, 15849, 19807, 23799, 36315, 37915, 47331, 211219
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

Original name was "Palindromic wing primes (a.k.a. near-repdigit palindromes) of the form 7*(10^a(n)-1)/9-2*10^[ a(n)/2 ]."
Prime versus probable prime status and proofs are given in the author's table.
a(16) > 2*10^5. - Robert Price, Jun 23 2017
1 could be considered part of this sequence since the formula evaluates to 5 which is a degenerate form of the near-repdigit palindrome 777...77577...777 that has zero occurrences of the digit 7. - Robert Price, Jun 23 2017

Examples

			15 is in the sequence because 7*(10^15 - 1)/9 - 2*10^7 = 777777757777777 is prime.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(7*10^n - 18*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 40000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183180(n) + 1.

Extensions

a(15) from Robert Price, Jun 23 2017
Example edited by Jon E. Schoenfield, Jun 23 2017
Name edited by Jon E. Schoenfield, Jun 24 2017
a(16) from Robert Price, Oct 12 2023

A077786 Numbers k such that (10^k - 1) - 4*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

177, 225, 397, 1245, 8457, 20105, 111725
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

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

Examples

			177 is a term because (10^177 - 1) - 4*10^88 = 99...99599...99.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[10^n - 4*10^Floor[n/2] - 1], Print[n]], {n, 3, 20200, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183186(n) + 1.

Extensions

One more term from PWP table added by Patrick De Geest, Nov 05 2014
Name corrected by Jon E. Schoenfield, Oct 31 2018

A077788 Numbers k such that 7*(10^k - 1)/9 - 10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

9, 11, 17, 23, 2489, 3371, 4019, 29315, 30237, 40665, 101661, 150125
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

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

Examples

			11 is a term because 7*(10^11 - 1)/9 - 10^5 = 77777677777.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(7*10^n - 9*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 30300, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183181(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018
a(10) from Robert Price, Oct 07 2023
a(11) from Robert Price, Oct 17 2023
a(12) from Robert Price, Dec 06 2023

A077789 Numbers k such that (10^k - 1)/9 + 6*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

7, 67, 623, 5867, 44471, 78331, 83171
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
a(8) > 10^5. - Robert Price, Apr 30 2017

Examples

			7 is a term because (10^7 - 1)/9 + 6*10^3 = 1117111.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(10^n + 54*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 6000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A107127(n) + 1.

Extensions

a(5)-a(7) from Robert Price, Apr 30 2017
Name corrected by Jon E. Schoenfield, Oct 31 2018

A077790 Numbers k such that (10^k - 1)/3 + 4*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 7, 15, 23, 27, 35, 59, 63, 67, 155, 1867, 3111, 23517, 235415
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
a(14) > 200000. - Robert Price, Dec 29 2016

Examples

			23 is a term because (10^23 - 1)/3 + 4*10^11 = 33333333333733333333333.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(10^n + 12*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 23600, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183176(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018
a(14) from Robert Price, Oct 30 2023

A077791 Numbers k such that (10^k - 1)/9 + 7*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 9, 13, 15, 769, 1333, 1351, 6331, 262041
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

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

Examples

			13 is a term (10^13 - 1)/9 + 7*10^6 = 1111118111111.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(10^n + 63*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 6400, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A107648(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018
a(9) from Robert Price, Aug 03 2024

A077792 Numbers k such that (10^k - 1)/3 + 5*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 15, 171, 189, 547, 713, 2155, 3595, 13517, 60465
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.
a(11) > 2*10^5. - Robert Price, Apr 21 2016

Examples

			15 is a term because (10^15 - 1)/3 + 5*10^7 = 333333383333333.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(10^n + 15*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 13600, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183177(n) + 1.

Extensions

a(10) from Robert Price, Apr 21 2016
Name corrected by Jon E. Schoenfield, Oct 31 2018

A077793 Numbers k such that 7*(10^k - 1)/9 + 10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 7, 79, 109, 337, 481, 10657, 12319, 49351, 104455, 227775
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

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

Examples

			7 is a term because 7*(10^7 - 1)/9 + 10^3 = 7778777.

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[ If[ PrimeQ[(7*10^n + 9*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 12400, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183182(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018
a(9) from Robert Price, Oct 07 2023
a(10) from Robert Price, Oct 30 2023
a(11) from Robert Price, Aug 03 2024
Previous Showing 21-30 of 45 results. Next

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