A193890 -id:A193890 - cp's OEIS frontend

A007090 Numbers in base 4.

0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 123, 130, 131, 132, 133, 200, 201, 202, 203, 210, 211, 212, 213, 220, 221, 222, 223, 230, 231, 232, 233, 300, 301, 302, 303, 310, 311, 312, 313, 320, 321, 322, 323, 330, 331, 332, 333

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

Nonnegative integers with no decimal digit > 3. Thus nonnegative integers in base 10 whose tripling (trebling) by normal addition or multiplication requires no carry operation. - Rick L. Shepherd, Jun 25 2009

Interpreted in base 10: a(x)+a(y) = a(z) => x+y = z. The converse is not true in general. - Karol Bacik, Sep 27 2012

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Nathaniel Johnston, Table of n, a(n) for n = 0..10000
R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992
Index entries for 10-automatic sequences.

Cf. A007608, A000042, A007088 (base 2), A007089 (base 3), A007091 (base 5), A007092 (base 6), A007093 (base 7), A007094 (base 8), A007095 (base 9), A193890, A107715.

a007090 0 = 0
a007090 n = 10 * a007090 n' + m where (n', m) = divMod n 4
-- Reinhard Zumkeller, Apr 08 2013, Aug 11 2011

A007090 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n,base,4): return op(convert(l,base,10,10^nops(l))): end: seq(A007090(n),n=0..54); # Nathaniel Johnston, May 06 2011

Table[ FromDigits[ IntegerDigits[n, 4]], {n, 0, 60}]

a(n)=if(n<1,0,if(n%4,a(n-1)+1,10*a(n/4)))

A007090(n)=sum(i=1,#n=digits(n,4),n[i]*10^(#n-i)) \\ M. F. Hasler, Jul 25 2015 (Corrected by Jinyuan Wang, Oct 02 2019)

apply( A007090(n)=fromdigits(digits(n,4)), [0..66]) \\ M. F. Hasler, Nov 18 2019

a(n) = Sum_{d(i)*10^i: i=0, 1, ..., m}, where Sum_{d(i)*4^i: i=0, 1, ..., m} is the base 4 representation of n.

a(0) = 0, a(n) = 10*a(n/4) if n==0 (mod 4), a(n) = a(n-1)+1 otherwise. - Benoit Cloitre, Dec 22 2002

A107715 Primes having only {0,1,2,3} as digits.

Original entry on oeis.org

2, 3, 11, 13, 23, 31, 101, 103, 113, 131, 211, 223, 233, 311, 313, 331, 1013, 1021, 1031, 1033, 1103, 1123, 1201, 1213, 1223, 1231, 1301, 1303, 1321, 2003, 2011, 2111, 2113, 2131, 2203, 2213, 2221, 2311, 2333, 3001, 3011, 3023, 3121, 3203, 3221, 3301, 3313

Offset: 1

Rick L. Shepherd, May 22 2005

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)

Subsequence of A036956.
Cf. A036953 (primes containing digits from set {0, 1, 2}).
Cf. A010051, A007090, A193890, A385776.

a107715 n = a107715_list !! (n-1)
a107715_list = filter ((== 1) . a010051) a007090_list
-- Reinhard Zumkeller, Aug 11 2011

Select[Prime[Range[500]],Max[IntegerDigits[#]]<4&] (* Harvey P. Dale, May 09 2012 *)
Select[FromDigits/@Tuples[{0,1,2,3},4],PrimeQ] (* Harvey P. Dale, Mar 06 2016 *)

from gmpy2 import digits
from sympy import isprime
[int(digits(n,4)) for n in range(1000) if isprime(int(digits(n,4)))] # Chai Wah Wu, Jul 31 2014

print(list(islice(primes_with("0123"), 41))) # uses function/imports in A385776. Jason Bard, Jul 18 2025

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A007090 Numbers in base 4.

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A107715 Primes having only {0,1,2,3} as digits.

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