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 1-3 of 3 results.

A089375 Duplicate of A069582.

Original entry on oeis.org

31, 421, 71, 131, 191, 2551, 311, 391331, 431, 48241612864321, 911371, 971, 1031
Offset: 1

Views

Author

Keywords

A089374 Numbers n such that the concatenation (in descending order) of all the divisors of n, with 1 in the least significant position, is prime (or 1).

Original entry on oeis.org

1, 3, 4, 7, 13, 19, 25, 31, 39, 43, 48, 91, 97, 103, 109, 117, 151, 157, 181, 193, 211, 241, 244, 247, 271, 289, 292, 301, 309, 325, 337, 349, 367, 388, 409, 421, 439, 487, 523, 547, 571, 597, 601, 613, 628, 631, 633, 687, 691, 703, 711, 733, 769, 772, 793, 811
Offset: 1

Views

Author

Amarnath Murthy, Nov 08 2003

Keywords

Comments

See A176558(n) = reverse concatenation of divisors of n. See A175355 for corresponding values of reverse concatenations. Complement of A175354(n) for n >= 2. - Jaroslav Krizek, Apr 20 2010
If prime p divides n, then the exponent of p in the prime factorization of n is odd if p == 1 (mod 3) and even if p == 2 (mod 3). In particular, the sequence has no terms == 2 (mod 3). - Robert Israel, Apr 21 2020

Examples

			4 is a term as 421 is prime; 39 is a term as concatenation of 39,13,3 and 1, i.e. 391331, is prime.
25 is a member as 2551 is prime.
Divisors of 39 are 1,3,13,39; reverse concatenation of divisors 391331 is prime.
48 is a member as 48241612864321 is a prime.
		

Crossrefs

Cf. A069582, A323427 (primes p such that p^2 is in the sequence).

Programs

  • Maple
    select(n->isprime(parse(cat("",op(sort([op(numtheory[divisors](n))],`>`))))),[$1..3000])[]; (Alec Mihailovs, Aug 14 2005)
  • Mathematica
    Join[{1},Select[Range[1000],PrimeQ[FromDigits[Flatten[IntegerDigits/@Reverse[Divisors[ #]]]]]&]] (* Harvey P. Dale, Feb 11 2024 *)

Extensions

Corrected and extended by David Wasserman, Sep 15 2005
Edited by N. J. A. Sloane, Apr 29 2007, Aug 14 2010

A175355 Noncomposite reverse concatenations of divisors of n, sorted by n.

Original entry on oeis.org

1, 31, 421, 71, 131, 191, 2551, 311, 391331, 431, 48241612864321, 911371, 971, 1031, 1091, 1173913931, 1511, 1571, 1811, 1931, 2111, 2411, 24412261421, 24719131, 2711, 289171, 29214673421, 3014371, 30910331, 32565251351, 3371, 3491, 3671
Offset: 1

Views

Author

Jaroslav Krizek, Apr 20 2010

Keywords

Examples

			For n = 9; a(9) = 391331 because A089374(9) = 39 and divisors of 39 are 1, 3, 13, 39; reverse concatenation of divisors A176558(21) = 391331 is noncomposite.
		

Crossrefs

Subsequence of A176558(n). Supersequence of A055781.

Programs

  • Maple
    rcd:= proc(n) local D,T,i;
      D:= sort(convert(numtheory:-divisors(n),list));
      T:= D[1];
      for i from 2 to nops(D) do
        T:= T + 10^(1+ilog10(T))*D[i]
      od;
      T
    end proc:
    select(t -> t=1 or isprime(t), map(rcd, [$1..1000])); # Robert Israel, Aug 12 2020

Formula

a(n) = A176558(A089374(n)).
a(n) = A069582(n-1), n>1. [R. J. Mathar, May 03 2010]

Extensions

Edited by Charles R Greathouse IV, Apr 30 2010
Showing 1-3 of 3 results.