A281150 -id:A281150 - cp's OEIS frontend

A281225 The decimal representation of the Elias delta code for n (A281150(n)).

1, 8, 9, 20, 21, 22, 23, 192, 193, 194, 195, 196, 197, 198, 199, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857

Offset: 1

Indranil Ghosh, Jan 18 2017

			For n = 6, The Elias delta code for 6 is "10110" which is 22 in decimal. So, a(6) = 22.

Indranil Ghosh, Table of n, a(n) for n = 1..10000
J. Nelson Raja, P. Jaganathan and S. Domnic, A New Variable-Length Integer Code for Integer Representation and Its Application to Text Compression, Indian Journal of Science and Technology, Vol 8(24), September 2015.

Cf. A171885 (Decimal representation of the Elias gamma code for n), A281150, A281223.

def unary(n):
    return "1"*(n-1)+"0"
def elias_gamma(n):
    if n==1:
        return "1"
    k=int(math.log(n, 2))
    fp=unary(1+k)    #fp is the first part
    sp=n-2**(k)      #sp is the second part
    nb=k             #nb is the number of bits used to store sp in binary
    sp=bin(sp)[2:]
    if len(sp)

A281193 Elias's omega code for n.

Original entry on oeis.org

0, 100, 110, 101000, 101010, 101100, 101110, 1110000, 1110010, 1110100, 1110110, 1111000, 1111010, 1111100, 1111110, 10100100000, 10100100010, 10100100100, 10100100110, 10100101000, 10100101010, 10100101100, 10100101110, 10100110000, 10100110010, 10100110100

Offset: 1

Indranil Ghosh, Jan 17 2017

The idea of the Elias omega code is similar to that of the Elias delta code (A281150), except that the length of the codeword in the omega code is recursively encoded.

The number of bits in a(n) is equal to A072464(n).

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Khalid Sayood (Editor), Lossless Compression Handbook, Chapter 3 - Universal Codes, p. 59, section 3.6.
Wikipedia, Elias omega coding

Cf. A072464, A281149, A281150.

def E(n):
    s=""
    if n==1:
        return "0"
    else:
        b=(bin(n)[2:])
        s+=E(len(b)-1)+b
    return s
def elias_omega(n):
    return int(E(n)[1:]+"0")

A140341 The number of bits needed to write the universal code for an Elias delta coding, the simplest asymptotically optimal code.

Original entry on oeis.org

1, 4, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11

Offset: 1

David A. Scott (biject.bwts(AT)gmail.com), May 29 2008

A129972 is the number of bits for Elias gamma coding 1, 3, 3, 5 and A130233 is the number of bits for Fibonacci coding of integers 2, 3, 4, 4, 5, But Elias gamma and Fibonacci coding are not asymptotically optimal.

			The Elias Delta Code for 10 is '11000010', having 8 bits. So, a(10) = 8. - _Indranil Ghosh_, Jan 17 2017

David Salomon, Variable-length Codes for Data Compression, Springer Verlag, 2007, 191 pp.

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Debra A. Lelewer and Daniel S. Hirschberg, Data Compression. See Section 3, Elias Delta.
Hugh E. Williams and Justin Zobel, Compressing integers for fast file access, The Computer Journal 42 (1999), pp. 193-201.

Cf. A281150 - Indranil Ghosh, Jan 17 2017

a(n)=my(b=log(n+.5)\log(2));b+log(b+1.5)\log(2)*2+1 \\ Charles R Greathouse IV, Mar 21 2012

A281313 Write n in Elias's delta code, interchange the 1's and 0's and convert it back to decimal.

Original entry on oeis.org

0, 7, 6, 11, 10, 9, 8, 63, 62, 61, 60, 59, 58, 57, 56, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 191, 190, 189, 188, 187, 186, 185, 184, 183, 182, 181, 180, 179, 178, 177, 176, 175, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 164, 163, 162

Offset: 1

Indranil Ghosh, Jan 19 2017

			For n = 10, the Elias delta code for 10 is '11000010' and after interchanging the 0's and 1's it becomes '00111101'. Now, 111101_2 = 61_10. So, a(10) = 61.

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Cf. A035327, A054429 (n is converted to Elias gamma code, the 1's and 0's are interchanged and the code is converted back to decimal, for n>1), A281150.

def a(n):
    s=""
    for i in A281150(n):
        if i=="1":
            s+="0"
        else:
            s+="1"
    return int(s, 2)

A281380 Numbers which are palindromic in their Elias delta code representation.

Original entry on oeis.org

1, 3, 5, 11, 19, 43, 91, 123, 135, 327, 455, 551, 935, 1127, 1383, 1767, 2023, 2071, 2839, 3223, 3991, 4183, 4695, 5463, 5975, 6359, 6871, 7639, 8151, 8247, 9783, 10551, 12087, 12471, 14007, 14775, 16311, 16503, 17527, 19063, 20087, 20855, 21879, 23415, 24439, 24823, 25847, 27383

Offset: 1

Indranil Ghosh, Jan 21 2017

Number n, such that A281150(n) is palindromic.

			43 is in the sequence because Elias delta code for 43 is '1101001011' and '1101001011' is palindromic.

Indranil Ghosh, Table of n, a(n) for n = 1..1012

Cf. A006995, A281150, A281379.

i=1
j=1
while j<=1012:
    if  A281150(i)==A281150(i)[::-1] :
        print(str(j)+" "+str(i))
        j+=1
    i+=1

A380934 Elias delta encoding of n converted from base 2 to integer.

Original entry on oeis.org

1, 4, 5, 12, 13, 14, 15, 32, 33, 34, 35, 36, 37, 38, 39, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219

Offset: 1

Darío Clavijo, Apr 21 2025

This is the Elias delta coding of n with leading zeros omited.

			For n = 16 a(16) = 80 because:
16 = 10000_2 and
Strip leading bit of n = 0000_2.
16 is of bitsize 5.
Prepend 5-1 zeros and 5 as 101_2
0000101_2 + 0000_2 = 00001010000_2 = 80.

Wikipedia, Elias delta coding

Cf. A281150.

A380934[n_] := FromDigits[Join[IntegerDigits[BitLength[n], 2], Rest[IntegerDigits[n, 2]]], 2] (* James C. McMahon, Apr 30 2025 *)

def a(n):
    if n == 1: return 1
    b = bin(n)[2:]
    L = len(b)
    g = '0' * (L - 1) + bin(L)[2:]
    d = g + b[1:]
    return int(d,2)
print([a(n) for n in range(1,60)])

def A380934(n): return int(bin(n.bit_length())+bin(n)[3:],2) # Chai Wah Wu, Apr 21 2025

cp's OEIS Frontend

A281225 The decimal representation of the Elias delta code for n (A281150(n)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A281193 Elias's omega code for n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Python

A140341 The number of bits needed to write the universal code for an Elias delta coding, the simplest asymptotically optimal code.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

PARI

A281313 Write n in Elias's delta code, interchange the 1's and 0's and convert it back to decimal.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A281380 Numbers which are palindromic in their Elias delta code representation.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

A380934 Elias delta encoding of n converted from base 2 to integer.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

Python