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.

User: Matevz Markovic

Matevz Markovic's wiki page.

Matevz Markovic has authored 4 sequences.

A238378 Numbers k such that (k+1)^(k-1) + k is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 8, 158, 536, 4670, 9795
Offset: 1

Views

Author

Matevz Markovic, Feb 25 2014

Keywords

Comments

Next term is >= 30000.

Examples

			3 is in the sequence since (3+1)^(3-1) + 3 = 4^2 + 3 = 19 is prime.

Crossrefs

Cf. A187602 (corresponding primes).

Programs

  • Mathematica
    Select[Range[600],PrimeQ[(#+1)^(#-1)+#]&] (* The program generates the first eight terms of the sequence. *) (* Harvey P. Dale, Feb 07 2024 *)
  • PARI
    is(n)=isprime((n+1)^(n-1)+n) \\ Charles R Greathouse IV, Jun 06 2017

A192261 Numbers n such that 4n+1 is a palindromic prime.

Original entry on oeis.org

1, 25, 45, 78, 88, 93, 189, 199, 232, 2575, 2625, 2650, 3105, 3180, 3205, 3585, 3685, 4015, 4090, 4140, 4165, 4545, 4620, 7753, 7878, 8383, 8763, 8788, 8838, 8938, 9318, 9393, 9823, 17829, 17979, 18259, 18309, 18409, 18889, 19344, 19369, 19494, 19849, 19924
Offset: 1

Views

Author

Matevz Markovic, Jul 02 2011

Keywords

Links

Crossrefs

Cf. A002385, A002144, A081220.

Programs

  • Mathematica
    Select[Range[10000],PrimeQ[4#+1]&&PalindromeQ[4#+1]&] (* Harvey P. Dale, Jun 24 2023 *)
  • PARI
    is(n)=n==eval(concat(Vecrev(Str(n))))&&isprime(n);
for(n=1, 1e4, if(is(4*n+1), print1(n, ", "))) \\ Altug Alkan, Nov 04 2015

Formula

{n such that A016813(n) is in A002385}. [Jonathan Vos Post, Jul 17 2011]

Extensions

Prior Mathematica program removed and more terms from Harvey P. Dale, Jun 24 2023

A172413 Positive numbers n such that 11^n + n + 1 is prime.

Original entry on oeis.org

1, 29, 35, 1309, 84379
Offset: 1

Views

Author

Matevz Markovic, Jun 30 2011

Keywords

Comments

11^n + n + 1 for n = 84379 is a probable prime.
There are no further terms up to 100000.

Crossrefs

Cf. A005808, A046867, A109076.

Programs

  • Mathematica
    Do[ If[PrimeQ[11^m + m + 1 ] , Print[m]], {m, 5000}]
  • PARI
    is(n)=ispseudoprime(11^n+n+1) \\ Charles R Greathouse IV, Jun 13 2017

A186080 Fourth powers that are palindromic in base 10.

Original entry on oeis.org

0, 1, 14641, 104060401, 1004006004001, 10004000600040001, 100004000060000400001, 1000004000006000004000001, 10000004000000600000040000001, 100000004000000060000000400000001, 1000000004000000006000000004000000001, 10000000004000000000600000000040000000001, 100000000004000000000060000000000400000000001
Offset: 1

Views

Author

Matevz Markovic, Feb 11 2011

Keywords

Comments

See A056810 (the main entry for this problem) for further information, including the search limit. - N. J. A. Sloane, Mar 07 2011
Conjecture: If k^4 is a palindrome > 0, then k begins and ends with digit 1, all other digits of k being 0.
The number of zeros in 1x1, where the x are zeros, is the same as (the number of zeros)/4 in (1x1)^4 = 1x4x6x4x1.

Links

  • P. De Geest, Palindromic cubes (The Simmons test is mentioned here) [broken link]
  • G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy]

Crossrefs

Cf. A002113, A168576, A056810, A002778, A002779.

Programs

  • Magma
    [ p: n in [0..10000000] | s eq Reverse(s) where s is Intseq(p) where p is n^4 ];
  • Mathematica
    Do[If[Module[{idn = IntegerDigits[n^4, 10]}, idn == Reverse[idn]], Print[n^4]], {n, 100000001}]

Formula

a(n) = A056810(n)^4.

Extensions

a(11)-a(13) using extensions of A056810 from Hugo Pfoertner, Oct 22 2021

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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