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 1-5 of 5 results.

A004094 Powers of 2 written backwards.

Original entry on oeis.org

1, 2, 4, 8, 61, 23, 46, 821, 652, 215, 4201, 8402, 6904, 2918, 48361, 86723, 63556, 270131, 441262, 882425, 6758401, 2517902, 4034914, 8068838, 61277761, 23445533, 46880176, 827712431, 654534862, 219078635, 4281473701, 8463847412, 6927694924, 2954399858, 48196897171
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Freeman Dyson believes that A014963(a(n)) <> 5 is true but cannot be proved, see link. - Reinhard Zumkeller, Jan 05 2005

Links

Crossrefs

Cf. A014963, A102382, A102383, A102384, A102385.
The following are parallel families: A000079 (2^n), A004094 (2^n reversed), A028909 (2^n sorted up), A028910 (2^n sorted down), A036447 (double and reverse), A057615 (double and sort up), A263451 (double and sort down); A000244 (3^n), A004167 (3^n reversed), A321540 (3^n sorted up), A321539 (3^n sorted down), A163632 (triple and reverse), A321542 (triple and sort up), A321541 (triple and sort down).
Cf. A004086 (read n backwards).
For indices of primes see A057708.

Programs

  • Haskell
    a004094 = a004086 . a000079  -- Reinhard Zumkeller, Apr 02 2014
  • Magma
    [Seqint(Reverse(Intseq(2^n))): n in [0..35]]; // Vincenzo Librandi, Jan 22 2020
  • Maple
    a:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||(2^n)):
seq(a(n), n=0..50);  # Alois P. Heinz, Jan 21 2020
  • Mathematica
    Table[FromDigits[Reverse[IntegerDigits[2^n]]], {n, 0, 35}] (* Vincenzo Librandi, Jan 22 2020 *)
  • PARI
    rev(n)=subst(Polrev(digits(n)),'x,10)
a(n)=rev(2^n) \\ Charles R Greathouse IV, Oct 20 2014
  • PARI
    apply( {A004094(n)=fromdigits(Vecrev(digits(2^n)))}, [0..44]) \\ M. F. Hasler, Feb 18 2021
  • Python
    def A004094(n):
    return int(str(2**n)[::-1]) # Chai Wah Wu, Feb 19 2021

Formula

a(n) = A004086(A000079(n)). - Reinhard Zumkeller, Apr 02 2014

Extensions

More terms from Reinhard Zumkeller, Jan 05 2005

A102382 a(n) = A001221(A004094(n)).

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 3, 2, 1, 4, 3, 4, 4, 4, 3, 1, 4, 4, 5, 2, 2, 2, 3, 3, 3, 2, 2, 3, 1, 2, 5, 4, 4, 3, 4, 4, 1, 4, 2, 4, 4, 3, 3, 3, 4, 2, 1, 3, 3, 4, 6, 5, 2, 4, 4, 4, 2, 3, 5, 5, 3, 1, 6, 4, 3, 4, 6, 3, 1, 4, 4, 4, 5, 4, 4, 3, 2, 2, 3, 3, 3, 6, 3, 4, 4, 3, 4, 4, 4, 3, 8, 3, 4, 5, 3, 4
Offset: 0

Views

Author

Reinhard Zumkeller, Jan 06 2005

Keywords

Examples

			n = 19: reverse(2^19) = 882425 = 5^2*47*751, so a(19) = 3.
n = 38: reverse(2^38) = 449609778472 = 2^3*56201222309, so a(38) = 2. - _Sean A. Irvine_, Sep 26 2023

Crossrefs

Cf. A001221, A004094, A102383, A102384, A102385.

Programs

  • Mathematica
    a[n_] := PrimeNu[IntegerReverse[2^n]]; Array[a, 100, 0] (* Amiram Eldar, Oct 02 2024 *)
  • PARI
    a(n) = omega(fromdigits(Vecrev(digits(2^n)))); \\ Amiram Eldar, Oct 02 2024

Extensions

a(38) corrected by Sean A. Irvine, Sep 26 2023

A102383 a(n) = A001222(A004094(n)).

Original entry on oeis.org

0, 1, 2, 3, 1, 1, 2, 1, 3, 2, 1, 2, 4, 2, 2, 3, 3, 1, 4, 4, 4, 4, 4, 3, 1, 4, 7, 5, 2, 2, 2, 4, 4, 3, 2, 2, 3, 1, 4, 5, 4, 6, 3, 4, 4, 1, 4, 2, 4, 4, 3, 3, 3, 4, 2, 1, 3, 3, 4, 7, 6, 4, 5, 4, 4, 2, 3, 5, 7, 3, 1, 9, 4, 3, 4, 6, 4, 1, 4, 4, 4, 5, 6, 4, 3, 2, 2, 3, 3, 5, 6, 3, 4, 4, 3, 4, 4, 4, 3, 12, 3, 6, 5, 3, 5
Offset: 0

Views

Author

Reinhard Zumkeller, Jan 06 2005

Keywords

Examples

			n = 26: reverse(2^26) = 46880176 = 2^4*7*641*653, so a(26) = 7.
n = 38: reverse(2^38) = 449609778472 = 2^3*56201222309, so a(38) = 4. - _Sean A. Irvine_, Sep 26 2023

Crossrefs

Cf. A001222, A004094, A102382, A102384, A102385.

Programs

  • Mathematica
    a[n_] := PrimeOmega[IntegerReverse[2^n]]; Array[a, 100, 0] (* Amiram Eldar, Oct 02 2024 *)
  • PARI
    a(n) = bigomega(fromdigits(Vecrev(digits(2^n)))); \\ Amiram Eldar, Oct 02 2024

Extensions

a(38) corrected by Sean A. Irvine, Sep 26 2023

A102384 a(n) = A020639(A004094(n)).

Original entry on oeis.org

1, 2, 2, 2, 61, 23, 2, 821, 2, 5, 4201, 2, 2, 2, 137, 7, 2, 270131, 2, 5, 13, 2, 2, 2, 61277761, 17, 2, 7, 2, 5, 3373, 2, 2, 2, 113647, 53, 2, 274359834731, 2, 5, 109, 2, 2, 2, 19, 23888027348153, 7, 34613, 2, 5, 7, 2, 2, 1091, 919, 86936981079782063, 139, 29
Offset: 0

Views

Author

Reinhard Zumkeller, Jan 06 2005

Keywords

Examples

			n = 25 -> 2^25 = 33554432 -> 23445533 = 17*23*61*983: a(25) = 17.

Crossrefs

Cf. A004094, A020639, A102382, A102383, A102385.

Programs

  • Mathematica
    a[n_] := FactorInteger[IntegerReverse[2^n]][[1, 1]]; Array[a, 60, 0] (* Amiram Eldar, Oct 02 2024 *)
  • PARI
    a(n) = if(n == 0, 1, factor(fromdigits(Vecrev(digits(2^n))))[1,1]); \\ Amiram Eldar, Oct 02 2024

Extensions

Corrected by T. D. Noe, Nov 15 2006

A379938 Numbers k such that the k-th prime is a power of two reversed.

Original entry on oeis.org

1, 9, 18, 142, 575, 23652, 3633466, 10846595429, 802467018101, 2289255503212477
Offset: 1

Views

Author

Kalle Siukola, Jan 06 2025

Keywords

Examples

			The 9th prime is 23, 23 reversed is 32, and 32 = 2^5, so 9 is a term.

Crossrefs

Cf. A000040, A000079, A004087, A004094, A057708, A102385.

Programs

  • Python
    import sympy
for (k, p) in enumerate(sympy.primerange(10**8)):
    rev = int(str(p)[::-1])
    # is rev a power of two (or zero)?
    if rev & (rev - 1) == 0:
        print(k + 1, end=",")
print()

Formula

A000040(a(n)) = A102385(n).
a(n) = A000720(A102385(n)). - Michel Marcus, Jan 07 2025

Extensions

a(8)-a(10) from Amiram Eldar, Jan 07 2025
Showing 1-5 of 5 results.

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

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