A277820 -id:A277820 - cp's OEIS frontend

A277810 Square array A(r,c) = A019565(A277820(r,c)), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

2, 6, 3, 10, 15, 30, 210, 21, 14, 5, 22, 1155, 462, 35, 70, 858, 39, 910, 55, 330, 105, 1870, 3315, 72930, 5005, 2002, 33, 42, 9699690, 5187, 2926, 85, 714, 2145, 770, 7, 46, 111546435, 238602, 11305, 248710, 3927, 390, 77, 154, 4002, 87, 93763670, 21505, 152490, 440895, 3094, 91, 546, 231, 7130, 13485, 620310, 1078282205, 2306486, 9867, 114114, 17017, 170170, 1365, 2310

Offset: 1

Antti Karttunen, Nov 01 2016

Permutation of squarefree numbers (A005117) after their initial term 1.

			The top left corner of the array:
    2,    6,     10,   210,      22,    858,      1870,    9699690
    3,   15,     21,  1155,      39,   3315,      5187,  111546435
   30,   14,    462,   910,   72930,   2926,    238602,   93763670
    5,   35,     55,  5005,      85,  11305,     21505, 1078282205
   70,  330,   2002,   714,  248710, 152490,   2306486,   60138078
  105,   33,   2145,  3927,  440895,   9867,   1870935,  691587897
   42,  770,    390,  3094,  114114, 520030,    162690,  581334754
    7,   77,     91, 17017,     133,  33649,     50141, 6685349671
  154,  546, 170170,   570,    6118, 254562, 357505330,   51269790
  231, 1365,   7293,  3135, 1312311, 983535,  11599797,  589602585

Antti Karttunen, Table of n, a(n) for n = 1..1540; the first 55 antidiagonals of the array

Transpose: A277809.
The topmost row: A123098, the leftmost column: A277811.
Cf. A005117, A019565, A277820.

(define (A277810 n) (A277810bi (A002260 n) (A004736 n)))
(define (A277810bi row col) (A019565 (A277820bi row col)))

A(r,c) = A019565(A277820(r,c)).

A277818 Index of the column where n is located in array A277820: a(n) = 1 + A268389(n).

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 1, 1, 2, 3, 1, 2, 1, 1, 4, 1, 5, 2, 1, 3, 1, 1, 2, 2, 1, 1, 3, 1, 2, 4, 1, 1, 2, 5, 1, 2, 1, 1, 3, 3, 1, 1, 2, 1, 4, 2, 1, 2, 1, 1, 6, 1, 2, 3, 1, 1, 3, 2, 1, 4, 1, 1, 2, 1, 3, 2, 1, 5, 1, 1, 2, 2, 1, 1, 4, 1, 2, 3, 1, 3, 1, 1, 2, 1, 7, 2, 1, 1, 2, 4, 1, 2, 1, 1, 3, 2, 1, 1, 3, 1, 2, 6, 1, 1, 4, 2, 1, 3, 1, 1, 2, 1, 2, 3, 1, 2, 1, 1, 5, 4

Offset: 1

Antti Karttunen, Nov 02 2016

Ordinal transform of A268671.

One more than A268389.
Cf. A277820.
Cf. A268671 for the other index, also A277822.

Scheme
```
(define (A277818 n) (+ 1 (A268389 n)))
```

a(n) = 1 + A268389(n).

A277819 Transpose of square array A277820.

Original entry on oeis.org

1, 2, 3, 7, 6, 5, 4, 9, 10, 15, 13, 12, 27, 30, 17, 14, 23, 20, 45, 34, 51, 11, 18, 57, 60, 119, 102, 85, 8, 29, 54, 75, 68, 153, 170, 255, 25, 24, 39, 90, 221, 204, 427, 510, 257, 26, 43, 40, 105, 238, 359, 340, 765, 514, 771, 31, 46, 125, 120, 187, 306, 937, 1020, 1799, 1542, 1285, 28, 33, 114, 135, 136, 461, 854, 1275, 1028, 2313, 2570, 3855

Offset: 1

Antti Karttunen, Nov 01 2016

See A277820.

			The top left 10 x 10 corner of the array:
    1,    2,    7,    4,   13,   14,   11,    8,    25,    26
    3,    6,    9,   12,   23,   18,   29,   24,    43,    46
    5,   10,   27,   20,   57,   54,   39,   40,   125,   114
   15,   30,   45,   60,   75,   90,  105,  120,   135,   150
   17,   34,  119,   68,  221,  238,  187,  136,   393,   442
   51,  102,  153,  204,  359,  306,  461,  408,   667,   718
   85,  170,  427,  340,  937,  854,  599,  680,  1965,  1874
  255,  510,  765, 1020, 1275, 1530, 1785, 2040,  2295,  2550
  257,  514, 1799, 1028, 3341, 3598, 2827, 2056,  6425,  6682
  771, 1542, 2313, 3084, 5911, 4626, 7453, 6168, 11051, 11822

Transpose: A277820.
Row 1: A065621, row 2: A277823.
Column 1: A001317.
Cf. A048724, A099884.

(define (A277819 n) (A277820bi (A004736 n) (A002260 n))) ;; Code for A277820bi given in A277820.

A277821 Inverse permutation to A277820.

Original entry on oeis.org

1, 3, 2, 10, 4, 5, 6, 36, 9, 8, 28, 14, 15, 21, 7, 136, 11, 27, 120, 19, 91, 105, 20, 44, 45, 55, 13, 78, 35, 12, 66, 528, 77, 17, 496, 90, 435, 465, 43, 53, 325, 351, 54, 406, 18, 65, 378, 152, 153, 171, 16, 210, 135, 34, 190, 300, 26, 119, 276, 25, 231, 253, 104, 2080, 118, 275, 2016, 32, 1891, 1953, 252, 324, 1653, 1711, 33

Offset: 1

Antti Karttunen, Nov 03 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16383
Index entries for sequences that are permutations of the natural numbers

Inverse: A277820.

Cf. A268671, A277818.

(define (A277821 n) (let ((row (A268671 n)) (col (A277818 n))) (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))

a(n) = (1/2) * ((c+r)^2 - r - 3*c + 2), where c = A277818(n), and r = A268671(n).

A048720 Multiplication table {0..i} X {0..j} of binary polynomials (polynomials over GF(2)) interpreted as binary vectors, then written in base 10; or, binary multiplication without carries.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 4, 3, 0, 0, 4, 6, 6, 4, 0, 0, 5, 8, 5, 8, 5, 0, 0, 6, 10, 12, 12, 10, 6, 0, 0, 7, 12, 15, 16, 15, 12, 7, 0, 0, 8, 14, 10, 20, 20, 10, 14, 8, 0, 0, 9, 16, 9, 24, 17, 24, 9, 16, 9, 0, 0, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 0, 0, 11, 20, 27, 32, 27, 20, 27, 32, 27, 20, 11, 0

Offset: 0

Antti Karttunen, Apr 26 1999

Essentially same as A091257 but computed starting from offset 0 instead of 1.
Each polynomial in GF(2)[X] is encoded as the number whose binary representation is given by the coefficients of the polynomial, e.g., 13 = 2^3 + 2^2 + 2^0 = 1101_2 encodes 1*X^3 + 1*X^2 + 0*X^1 + 1*X^0 = X^3 + X^2 + X^0. - Antti Karttunen and Peter Munn, Jan 22 2021
To listen to this sequence, I find instrument 99 (crystal) works well with the other parameters defaulted. - Peter Munn, Nov 01 2022

			Top left corner of array:
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ...
  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ...
  0  2  4  6  8 10 12 14 16 18 20 22 24 26 28 30 ...
  0  3  6  5 12 15 10  9 24 27 30 29 20 23 18 17 ...
  ...
From _Antti Karttunen_ and _Peter Munn_, Jan 23 2021: (Start)
Multiplying 10 (= 1010_2) and 11 (= 1011_2), in binary results in:
     1011
  *  1010
  -------
   c1011
  1011
  -------
  1101110  (110 in decimal),
and we see that there is a carry-bit (marked c) affecting the result.
In carryless binary multiplication, the second part of the process (in which the intermediate results are summed) looks like this:
    1011
  1011
  -------
  1001110  (78 in decimal).
(End)

Alois P. Heinz, Antidiagonals n = 0..200, flattened
Antti Karttunen, Scheme-program for computing this sequence.
N. J. A. Sloane, Transforms: Maple implementation of binary eXclusive OR (XORnos).
Index entries for sequences related to carryless arithmetic
Index entries for sequences related to polynomials in ring GF(2)[X]

Cf. A051776 (Nim-product), A091257 (subtable).
Carryless multiplication in other bases: A325820 (3), A059692 (10).
Ordinary {0..i} * {0..j} multiplication table: A004247 and its differences from this: A061858 (which lists further sequences related to presence/absence of carry in binary multiplication).
Carryless product of the prime factors of n: A234741.
Binary irreducible polynomials ("X-primes"): A014580, factorization table: A256170, table of "X-powers": A048723, powers of 3: A001317, rearranged subtable with distinct terms (comparable to A054582): A277820.
See A014580 for further sequences related to the difference between factorization into GF(2)[X] irreducibles and ordinary prime factorization of the integer encoding.
Row/column 3: A048724 (even bisection of A003188), 5: A048725, 6: A048726, 7: A048727; main diagonal: A000695.
Associated additive operation: A003987.
Equivalent sequences, as compared with standard integer multiplication: A048631 (factorials), A091242 (composites), A091255 (gcd), A091256 (lcm), A280500 (division).
See A091202 (and its variants) and A278233 for maps from/to ordinary multiplication.
See A115871, A115872 and A277320 for tables related to cross-domain congruences.

trinv := n -> floor((1+sqrt(1+8*n))/2); # Gives integral inverses of the triangular numbers
# Binary multiplication of nn and mm, but without carries (use XOR instead of ADD):
Xmult := proc(nn,mm) local n,m,s; n := nn; m := mm; s := 0; while (n > 0) do if(1 = (n mod 2)) then s := XORnos(s,m); fi; n := floor(n/2); # Shift n right one bit. m := m*2; # Shift m left one bit. od; RETURN(s); end;

trinv[n_] := Floor[(1 + Sqrt[1 + 8*n])/2];
Xmult[nn_, mm_] := Module[{n = nn, m = mm, s = 0}, While[n > 0, If[1 == Mod[n, 2], s = BitXor[s, m]]; n = Floor[n/2]; m = m*2]; Return[s]];
a[n_] := Xmult[(trinv[n] - 1)*((1/2)*trinv[n] + 1) - n, n - (trinv[n]*(trinv[n] - 1))/2];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Mar 16 2015, updated Mar 06 2016 after Maple *)

up_to = 104;
A048720sq(b,c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A048720list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0, oo, for(col=0, a, i++; if(i > up_to, return(v)); v[i] = A048720sq(col, a-col))); (v); };
v048720 = A048720list(up_to);
A048720(n) = v048720[1+n]; \\ Antti Karttunen, Feb 15 2021

a(n) = Xmult( (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n), (n-((trinv(n)*(trinv(n)-1))/2)) );
T(2b, c)=T(c, 2b)=T(b, 2c)=2T(b, c); T(2b+1, c)=T(c, 2b+1)=2T(b, c) XOR c - Henry Bottomley, Mar 16 2001
For n >= 0, A003188(2n) = T(n, 3); A003188(2n+1) = T(n, 3) XOR 1, where XOR is the bitwise exclusive-or operator, A003987. - Peter Munn, Feb 11 2021

A115872 Square array where row n gives all solutions k > 0 to the cross-domain congruence n*k = A048720(A065621(n),k), zero sequence (A000004) if no such solutions exist.

Original entry on oeis.org

1, 2, 1, 3, 2, 3, 4, 3, 6, 1, 5, 4, 7, 2, 7, 6, 5, 12, 3, 14, 3, 7, 6, 14, 4, 15, 6, 7, 8, 7, 15, 5, 28, 7, 14, 1, 9, 8, 24, 6, 30, 12, 15, 2, 15, 10, 9, 28, 7, 31, 14, 28, 3, 30, 7, 11, 10, 30, 8, 56, 15, 30, 4, 31, 14, 3, 12, 11, 31, 9, 60, 24, 31, 5, 60, 15, 6, 3, 13, 12, 48, 10, 62, 28, 56, 6, 62, 28, 12, 6, 5, 14, 13, 51, 11, 63, 30, 60, 7, 63, 30, 15, 7, 10, 7

Offset: 1

Antti Karttunen, Feb 07 2006

Here * stands for ordinary multiplication and X means carryless (GF(2)[X]) multiplication (A048720).
Square array is read by descending antidiagonals, as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
Rows at positions 2^k are 1, 2, 3, ..., (A000027). Row 2n is equal to row n.
Numbers on each row give a subset of positions of zeros at the corresponding row of A284270. - Antti Karttunen, May 08 2019

			Fifteen initial terms of rows 1 - 19 are listed below:
   1:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...
   2:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...
   3:  3,  6,  7,  12,  14,  15,  24,  28,  30,  31,  48,  51,  56,  60,  62, ...
   4:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...
   5:  7, 14, 15,  28,  30,  31,  56,  60,  62,  63, 112, 120, 124, 126, 127, ...
   6:  3,  6,  7,  12,  14,  15,  24,  28,  30,  31,  48,  51,  56,  60,  62, ...
   7:  7, 14, 15,  28,  30,  31,  56,  60,  62,  63, 112, 120, 124, 126, 127, ...
   8:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...
   9: 15, 30, 31,  60,  62,  63, 120, 124, 126, 127, 240, 248, 252, 254, 255, ...
  10:  7, 14, 15,  28,  30,  31,  56,  60,  62,  63, 112, 120, 124, 126, 127, ...
  11:  3,  6, 12,  15,  24,  27,  30,  31,  48,  51,  54,  60,  62,  63,  96, ...
  12:  3,  6,  7,  12,  14,  15,  24,  28,  30,  31,  48,  51,  56,  60,  62, ...
  13:  5, 10, 15,  20,  21,  30,  31,  40,  42,  45,  47,  60,  61,  62,  63, ...
  14:  7, 14, 15,  28,  30,  31,  56,  60,  62,  63, 112, 120, 124, 126, 127, ...
  15: 15, 30, 31,  60,  62,  63, 120, 124, 126, 127, 240, 248, 252, 254, 255, ...
  16:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...
  17: 31, 62, 63, 124, 126, 127, 248, 252, 254, 255, 496, 504, 508, 510, 511, ...
  18: 15, 30, 31,  60,  62,  63, 120, 124, 126, 127, 240, 248, 252, 254, 255, ...
  19:  7, 14, 28,  31,  56,  62,  63, 112, 119, 124, 126, 127, 224, 238, 248, ...

Transpose: A114388. First column: A115873.
Cf. A048720, A065621, A115857, A115871, A325565, A325566, A325567, A325568, A325570, A325571.
Cf. also arrays A277320, A277810, A277820, A284270.
A few odd-positioned rows: row 1: A000027, Row 3: A048717, Row 5: A115770 (? Checked for all values less than 2^20), Row 7: A115770, Row 9: A115801, Row 11: A115803, Row 13: A115772, Row 15: A115801 (? Checked for all values less than 2^20), Row 17: A115809, Row 19: A115874, Row 49: A114384, Row 57: A114386.

X[a_, b_] := Module[{A, B, C, x},
     A = Reverse@IntegerDigits[a, 2];
     B = Reverse@IntegerDigits[b, 2];
     C = Expand[
        Sum[A[[i]]*x^(i-1), {i, 1, Length[A]}]*
        Sum[B[[i]]*x^(i-1), {i, 1, Length[B]}]];
     PolynomialMod[C, 2] /. x -> 2];
T[n_, k_] := Module[{x = BitXor[n-1, 2n-1], k0 = k},
     For[i = 1, True, i++, If[n*i == X[x, i],
     If[k0 == 1, Return[i], k0--]]]];
Table[T[n-k+1, k], {n, 1, 14}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Jan 04 2022 *)

up_to = 120;
A048720(b,c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1,n+n-1);
A115872sq(n, k) = { my(x = A065621(n)); for(i=1,oo,if((n*i)==A048720(x,i),if(1==k,return(i),k--))); };
A115872list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A115872sq(col,(a-(col-1))))); (v); };
v115872 = A115872list(up_to);
A115872(n) = v115872[n]; \\ (Slow) - Antti Karttunen, May 08 2019

Example section added and the data section extended up to n=105 by Antti Karttunen, May 08 2019

A277320 Square array A(r,c) = A048720(A065621(r), c), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Original entry on oeis.org

1, 2, 2, 3, 4, 7, 4, 6, 14, 4, 5, 8, 9, 8, 13, 6, 10, 28, 12, 26, 14, 7, 12, 27, 16, 23, 28, 11, 8, 14, 18, 20, 52, 18, 22, 8, 9, 16, 21, 24, 57, 56, 29, 16, 25, 10, 18, 56, 28, 46, 54, 44, 24, 50, 26, 11, 20, 63, 32, 35, 36, 39, 32, 43, 52, 31, 12, 22, 54, 36, 104, 42, 58, 40, 100, 46, 62, 28, 13, 24, 49, 40, 101, 112, 49, 48, 125, 104, 33, 56, 21

Offset: 1

Antti Karttunen, Nov 01 2016

			The top left corner of the array:
   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12
   2,   4,   6,   8,  10,  12,  14,  16,  18,  20,  22,  24
   7,  14,   9,  28,  27,  18,  21,  56,  63,  54,  49,  36
   4,   8,  12,  16,  20,  24,  28,  32,  36,  40,  44,  48
  13,  26,  23,  52,  57,  46,  35, 104, 101, 114, 127,  92
  14,  28,  18,  56,  54,  36,  42, 112, 126, 108,  98,  72
  11,  22,  29,  44,  39,  58,  49,  88,  83,  78,  69, 116
   8,  16,  24,  32,  40,  48,  56,  64,  72,  80,  88,  96
  25,  50,  43, 100, 125,  86,  79, 200, 209, 250, 227, 172
  26,  52,  46, 104, 114,  92,  70, 208, 202, 228, 254, 184
  31,  62,  33, 124,  99,  66,  93, 248, 231, 198, 217, 132
  28,  56,  36, 112, 108,  72,  84, 224, 252, 216, 196, 144
  21,  42,  63,  84,  65, 126, 107, 168, 189, 130, 151, 252
  22,  44,  58,  88,  78, 116,  98, 176, 166, 156, 138, 232
  19,  38,  53,  76,  95, 106, 121, 152, 139, 190, 173, 212
  16,  32,  48,  64,  80,  96, 112, 128, 144, 160, 176, 192
  49,  98,  83, 196, 245, 166, 151, 392, 441, 490, 475, 332
  50, 100,  86, 200, 250, 172, 158, 400, 418, 500, 454, 344
  55, 110,  89, 220, 235, 178, 133, 440, 399, 470, 481, 356

Transpose: A277199.
Main diagonal: A277699.
Row 1: A000027, Row 3: A048727.
Column 1: A065621, Column 3: A277823, Column 5: A277825.
Cf. A277820 (array obtained by selecting only the columns with an index A001317(k), k=0..).
Cf. A048720, A115872.

(define (A277320 n) (A277320bi (A002260 n) (A004736 n)))
(define (A277320bi row col) (A048720bi (A065621 row) col))

A(r,c) = A048720(A065621(r), c).

A277823 a(n) = A048724(A065621(n)).

Original entry on oeis.org

3, 6, 9, 12, 23, 18, 29, 24, 43, 46, 33, 36, 63, 58, 53, 48, 83, 86, 89, 92, 71, 66, 77, 72, 123, 126, 113, 116, 111, 106, 101, 96, 163, 166, 169, 172, 183, 178, 189, 184, 139, 142, 129, 132, 159, 154, 149, 144, 243, 246, 249, 252, 231, 226, 237, 232, 219, 222, 209, 212, 207, 202, 197, 192, 323, 326, 329, 332, 343, 338, 349, 344, 363, 366, 353

Offset: 1

Antti Karttunen, Nov 01 2016

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences related to binary expansion of n

Cf. A048720, A065621.
Column 2 of A277820.
Column 3 of A277320.

def A277823(n): return (m:=n^ (n&~-n)<<1)^m<<1 # Chai Wah Wu, Jun 29 2022

(define (A277823 n) (A048724 (A065621 n)))
(define (A277823 n) (A048720bi (A065621 n) 3))
(define (A277823 n) (A277320bi n 3))

a(n) = A048724(A065621(n)).

a(n) = A277320(n,3) = A048720(A065621(n),3).

A277880 Dispersion of evil numbers: Square array A(r,c) with A(r,1) = A000069(r); and for c > 1, A(r,c) = A001969(1+(A(r,c-1))), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Original entry on oeis.org

1, 3, 2, 6, 5, 4, 12, 10, 9, 7, 24, 20, 18, 15, 8, 48, 40, 36, 30, 17, 11, 96, 80, 72, 60, 34, 23, 13, 192, 160, 144, 120, 68, 46, 27, 14, 384, 320, 288, 240, 136, 92, 54, 29, 16, 768, 640, 576, 480, 272, 184, 108, 58, 33, 19, 1536, 1280, 1152, 960, 544, 368, 216, 116, 66, 39, 21, 3072, 2560, 2304, 1920, 1088, 736, 432, 232, 132, 78, 43, 22

Offset: 1

Antti Karttunen, Nov 03 2016

			The top left 12 x 12 corner of the array:
   1,  3,  6,  12,  24,  48,   96,  192,  384,   768,  1536,  3072
   2,  5, 10,  20,  40,  80,  160,  320,  640,  1280,  2560,  5120
   4,  9, 18,  36,  72, 144,  288,  576, 1152,  2304,  4608,  9216
   7, 15, 30,  60, 120, 240,  480,  960, 1920,  3840,  7680, 15360
   8, 17, 34,  68, 136, 272,  544, 1088, 2176,  4352,  8704, 17408
  11, 23, 46,  92, 184, 368,  736, 1472, 2944,  5888, 11776, 23552
  13, 27, 54, 108, 216, 432,  864, 1728, 3456,  6912, 13824, 27648
  14, 29, 58, 116, 232, 464,  928, 1856, 3712,  7424, 14848, 29696
  16, 33, 66, 132, 264, 528, 1056, 2112, 4224,  8448, 16896, 33792
  19, 39, 78, 156, 312, 624, 1248, 2496, 4992,  9984, 19968, 39936
  21, 43, 86, 172, 344, 688, 1376, 2752, 5504, 11008, 22016, 44032
  22, 45, 90, 180, 360, 720, 1440, 2880, 5760, 11520, 23040, 46080

Inverse permutation: A277881.
Transpose: A277882.
Column 1: A000069, column 2: A129771.
Row 1: A003945.
Cf. A277813 (index of the row where n is located in this array), A277822 (index of the column).
Cf. A001969.
Other related tables or permutations: A277820, A277902, A248513.

(define (A277880 n) (A277880bi (A002260 n) (A004736 n)))
(define (A277880bi row col) (if (= 1 col) (A000069 row) (A001969 (+ 1 (A277880bi row (- col 1))))))
;; Alternatively:
(define (A277880bi row col) (cond ((= 1 col) (A000069 row)) ((= 2 col) (A129771 row)) (else (* 2 (A277880bi row (- col 1))))))
(define (A129771 n) (+ 1 (* 2 (A000069 n))))

A(r,1) = A000069(r) and for c > 1, A(r,c) = A001969(1+(A(r,c-1))).
Alternatively, if we set also the second column explicitly as:
   A(r,2) = A129771(r) = 1+ 2*A000069(r),
then the rest of entries in each row are obtained just by doubling the preceding term on the same row: A(r,c) = 2*A(r,c-1), for c >= 3.
As a composition of other permutations:
a(n) = A277902(A277820(n)).

A277825 a(n) = A048725(A065621(n)) = A048720(A065621(n),5).

Original entry on oeis.org

5, 10, 27, 20, 57, 54, 39, 40, 125, 114, 99, 108, 65, 78, 95, 80, 245, 250, 235, 228, 201, 198, 215, 216, 141, 130, 147, 156, 177, 190, 175, 160, 485, 490, 507, 500, 473, 470, 455, 456, 413, 402, 387, 396, 417, 430, 447, 432, 277, 282, 267, 260, 297, 294, 311, 312, 365, 354, 371, 380, 337, 350, 335, 320, 965, 970, 987, 980, 1017, 1014, 999, 1000

Offset: 1

Antti Karttunen, Nov 02 2016

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences related to binary expansion of n

Column 3 of A277820, Column 5 of A277320.

Cf. A048720, A048724, A048725, A065621, A277823.

def A277825(n): return (m:=n^ (n&~-n)<<1)^m<<2 # Chai Wah Wu, Jun 29 2022

(define (A277825 n) (A048724 (A277823 n)))
(define (A277825 n) (A048720bi (A065621 n) 5)) ;; For A048720bi see the Scheme-program attachment in A048720.

a(n) = A048724(A277823(n)) = A048725(A065621(n)).

a(n) = A048720(A065621(n),5).

cp's OEIS Frontend

A277810 Square array A(r,c) = A019565(A277820(r,c)), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

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A277818 Index of the column where n is located in array A277820: a(n) = 1 + A268389(n).

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A277819 Transpose of square array A277820.

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A277821 Inverse permutation to A277820.

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A048720 Multiplication table {0..i} X {0..j} of binary polynomials (polynomials over GF(2)) interpreted as binary vectors, then written in base 10; or, binary multiplication without carries.

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A115872 Square array where row n gives all solutions k > 0 to the cross-domain congruence n*k = A048720(A065621(n),k), zero sequence (A000004) if no such solutions exist.

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A277320 Square array A(r,c) = A048720(A065621(r), c), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

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A277823 a(n) = A048724(A065621(n)).

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