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 1-6 of 6 results.

A069582 Primes arising in A089374.

Original entry on oeis.org

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

Amarnath Murthy, Mar 24 2002

Keywords

Examples

			48241612864321 is the (prime) term generated by 48.

Crossrefs

Cf. A089374.

Extensions

More terms from Sascha Kurz, Feb 01 2003
Edited by N. J. A. Sloane, Oct 27 2008 at the suggestion of R. J. Mathar.

A176558 a(n) is the reverse concatenation of divisors of n.

Original entry on oeis.org

1, 21, 31, 421, 51, 6321, 71, 8421, 931, 10521, 111, 1264321, 131, 14721, 15531, 168421, 171, 1896321, 191, 20105421, 21731, 221121, 231, 2412864321, 2551, 261321, 27931, 28147421, 291, 30151065321, 311, 32168421, 331131, 341721, 35751, 361812964321, 371
Offset: 1

Views

Author

Jaroslav Krizek, Apr 20 2010

Keywords

Comments

Union of A089374(n) for n >= 1 and A175354(n) for n >= 2. - Jonathan Vos Post, Apr 17 2011

Examples

			For n=12; divisors of 12: 1,2,3,4,6,12; a(12)=1264321 (reverse concatenation).

Links

Crossrefs

Cf. A089374, A175354, A175355, A176588, A176589.

Programs

  • Maple
    a:= n-> parse(cat(sort([numtheory[divisors](n)[]], `>`)[])):
seq(a(n), n=0..40);  # Alois P. Heinz, Dec 31 2020
  • Mathematica
    Table[FromDigits@ Flatten@ Map[IntegerDigits, Reverse@ Divisors@ n], {n, 34}] (* Michael De Vlieger, Jan 23 2017 *)
  • PARI
    a(n) = {s = ""; fordiv(n, d, s = concat(Str(d), s)); eval(s);} \\ Michel Marcus, Feb 16 2015
  • Python
    from sympy import divisors
def a(n): return int("".join(str(d) for d in divisors(n)[::-1]))
print([a(n) for n in range(1, 35)]) # Michael S. Branicky, Dec 31 2020

Extensions

More terms from Charles R Greathouse IV, Apr 23 2010
Corrected by Jaroslav Krizek, Apr 26 2010
Edited by Charles R Greathouse IV, Apr 30 2010

A175354 Numbers m such that reverse concatenations of divisors of m are nonprimes.

Original entry on oeis.org

1, 2, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81
Offset: 1

Views

Author

Jaroslav Krizek, Apr 20 2010

Keywords

Comments

See A176558(n) = reverse concatenation of divisors of n. See A176588 for corresponding values of reverse concatenations. Complement of A089374(n) for n >= 2.

Examples

			Divisors of 12: 1, 2, 3, 4, 6, 12; reverse concatenation of divisors 1264321 is nonprime number.

Links

Crossrefs

Cf. A089374, A176558, A176588.

Programs

  • Maple
    filter:= proc(n) local r,L,i;
  L:= sort(convert(numtheory:-divisors(n),list));
  r:= L[1];
  for i from 2 to nops(L) do
   r:= r + 10^(1+ilog10(r))*L[i]
  od;
  not isprime(r)
end proc:
select(filter, [$1..100]); # Robert Israel, Apr 21 2020
  • Mathematica
    Select[Range[90],!PrimeQ[FromDigits[Flatten[IntegerDigits/@Reverse[Divisors[#]]]]]&] (* Harvey P. Dale, Mar 21 2025 *)
  • PARI
    rcd(n)=my(d=divisors(n));n=1;for(i=2,#d,n=glue(d[i],n));n
glue(a,b)=a*10^#Str(b)+b
for(m=1,81,if(!isprime(rcd(m)),print1(m", ")))

Extensions

Program, editing, and extension by Charles R Greathouse IV, Apr 23 2010
Corrected by Jaroslav Krizek, Apr 26 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.

Links

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

A176588 a(n) = A176558(A175354(n)) = numbers m as reverse concatenations of divisors of numbers from A175354, where A175354 = numbers k such that reverse concatenations of divisors of k are nonprimes.

Original entry on oeis.org

1, 21, 51, 6321, 8421, 931, 10521, 111, 1264321, 14721, 15531, 168421, 171, 1896321, 20105421, 21731, 221121, 231, 2412864321, 261321, 27931, 28147421, 291, 30151065321, 32168421, 331131, 341721, 35751, 361812964321, 371
Offset: 1

Views

Author

Jaroslav Krizek, Apr 21 2010

Keywords

Examples

			a(9) = 1264321 because A089374(9) = 12 and divisors of 12 are 1, 2, 3, 4, 6, 12; reverse concatenation of divisors A176558(12) = 1264321 is nonprime.

Crossrefs

Subsequence of A176558(n) = reverse concatenation of divisors of n.

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010

A176589 Numbers k such that both concatenation of divisors of k and reverse concatenation of divisors of k are noncomposite.

Original entry on oeis.org

1, 3, 7, 13, 31, 97, 103, 109, 151, 181, 193, 367, 409, 439, 487, 523, 571, 601, 613, 733, 811, 823, 1069, 1117, 1279, 1483, 1489, 1579, 1597, 1789, 1831, 1867, 1897, 1939, 2161, 2203, 2239, 2251, 2269, 2281, 2437, 2503, 2509, 2539, 2659, 2671, 2689, 2953
Offset: 1

Views

Author

Jaroslav Krizek, Apr 21 2010

Keywords

Comments

Numbers k such that both A037278(k) and A176558(k) are noncomposite.

Examples

			31 is a term; divisors of 31: 1, 31; both concatenation of divisors 131 and reverse concatenation of divisors 311 are noncomposite.
1897 is a term; divisors of 1897: 1, 7, 271, 1897; both concatenation of divisors 172711897 and reverse concatenation of divisors 189727171 are noncomposite.
Sequence of corresponding values of concatenations of divisors of a(n): 1, 13, 17, 113, 131, 197, ...
Sequence of corresponding values of reverse concatenations of divisors of a(n): 1, 31, 71, 131, 311, 971, ...

Crossrefs

Cf. A037278, A176558, A176553, A089374, A176590.

Formula

Intersection of A176553 and A089374. - Jason Yuen, Feb 08 2025

Extensions

Expanded and revised by Charles R Greathouse IV, Apr 24 2010
Showing 1-6 of 6 results.

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