A004094 Powers of 2 written backwards.

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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

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

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Edge Foundation, Annual Question 2005
• Richard Lipton, More on testing Dyson's conjecture (2014)
• N. J. A. Sloane, Exciting Number Sequences (video of talk), Mar 05 2021.

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