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 1-10 of 18 results. Next

A382725 Number of entries in the n-th row of Pascal's triangle not divisible by 8.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 5, 10, 9, 12, 11, 14, 14, 16, 5, 10, 13, 20, 13, 18, 20, 24, 11, 22, 20, 28, 22, 28, 28, 32, 5, 10, 13, 20, 17, 26, 28, 40, 13, 26, 26, 36, 28, 40, 40, 48, 11, 22, 28, 44, 28, 40, 44, 56, 22, 44, 40, 56, 44, 56, 56, 64, 5, 10, 13, 20, 17, 26, 28, 40, 17, 34, 34, 52, 36, 56, 56, 80, 13
Offset: 0

Views

Author

N. J. A. Sloane, Apr 23 2025

Keywords

Links

  • James G. Huard, Blair K. Spearman, and Kenneth S. Williams, Pascal's triangle (mod 8), European Journal of Combinatorics 19:1 (1998), pp. 45-62.

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382724.

Programs

  • Python
    def A382725(n):
    n1 = n>>1
    n2 = n1>>1
    np = ~n
    n100 = (n2&(~n1)&np).bit_count()
    n110 = (n2&n1&np).bit_count()
    n10 = (n1&np).bit_count()
    return ((n100+1<<3)+(n110<<1)+n10*(n10+3))<>3 # Chai Wah Wu, Aug 10 2025

A382731 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 8.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 28, 36, 41, 51, 60, 72, 83, 97, 111, 127, 132, 142, 155, 175, 188, 206, 226, 250, 261, 283, 303, 331, 353, 381, 409, 441, 446, 456, 469, 489, 506, 532, 560, 600, 613, 639, 665, 701, 729, 769, 809, 857, 868, 890, 918, 962, 990, 1030, 1074, 1130, 1152, 1196, 1236, 1292, 1336, 1392, 1448, 1512, 1517, 1527
Offset: 0

Views

Author

N. J. A. Sloane, Apr 23 2025

Keywords

Links

  • James G. Huard, Blair K. Spearman, and Kenneth S. Williams, Pascal's triangle (mod 8), European Journal of Combinatorics 19:1 (1998), pp. 45-62.

Crossrefs

Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382730.

Programs

  • Python
    def A382731(n):
    c = 0
    for m in range(n+1):
        n1 = m>>1
        n2 = n1>>1
        np = ~m
        n100 = (n2&(~n1)&np).bit_count()
        n110 = (n2&n1&np).bit_count()
        n10 = (n1&np).bit_count()
        c += ((n100+1<<3)+(n110<<1)+n10*(n10+3))<>3
    return c # Chai Wah Wu, Aug 10 2025

A386952 Number of entries in the n-th row of Pascal's triangle not divisible by 9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 4, 8, 12, 9, 12, 15, 14, 16, 18, 7, 14, 21, 14, 19, 24, 21, 24, 27, 4, 8, 12, 12, 18, 24, 20, 28, 36, 9, 18, 27, 20, 28, 36, 31, 38, 45, 14, 28, 42, 28, 38, 48, 42, 48, 54, 7, 14, 21, 20, 31, 42, 33, 48, 63, 14, 28, 42, 31, 44, 57, 48
Offset: 0

Views

Author

Chai Wah Wu, Aug 10 2025

Keywords

Links

  • James G. Huard, Blair K. Spearman, and Kenneth S. Williams, Pascal's triangle (mod 9), Acta Arithmetica, 78 (1997), 331-349.

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382725.

Programs

  • Python
    import re
from gmpy2 import digits
def A386952(n):
    s = digits(n,3)
    n1 = s.count('1')
    n2 = s.count('2')
    n01 = s.count('10')
    n02 = s.count('20')
    n11 = len(re.findall('(?=11)',s))
    n12 = s.count('21')
    return ((3*((1+n01<<2)+n11)+((n02<<2)+n12<<2))*3**n2<>2

A387050 Number of entries in the n-th row of Pascal's triangle not divisible by 16.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 9, 18, 15, 20, 17, 22, 21, 24, 21, 26, 25, 28, 27, 30, 30, 32, 9, 18, 23, 36, 21, 30, 33, 40, 25, 34, 35, 44, 37, 42, 44, 48, 21, 42, 37, 52, 37, 50, 48, 56, 43, 54, 52, 60, 54, 60, 60, 64, 9, 18, 23, 36, 29
Offset: 0

Views

Author

Chai Wah Wu, Aug 15 2025

Keywords

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382725, A386952.

Programs

  • Python
    def A387050(n):
    n1 = n>>1
    n2 = n1>>1
    n3 = n2>>1
    np = ~n
    n10, n100, n110 = (k1:=n1&np).bit_count(), (k2:=(k1>>1)&np).bit_count(), (k3:=n2&k1).bit_count()
    n1100, n1000, n1010, n1110 = (n3&k2).bit_count(), ((k2>>1)&np).bit_count(), ((k1>>2)&k1).bit_count(), (n3&k3).bit_count()
    return n10*(n10*(n10+3)+6*((n100<<2)+n110)+20)//6+((n1000<<2)+n100+n1010+n1100<<2)+n110+n1110+8<>3

A382721 Number of entries in the n-th row of Pascal's triangle not divisible by 11.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 8, 16, 24, 32
Offset: 0

Views

Author

N. J. A. Sloane, Apr 23 2025

Keywords

Links

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382722.

Programs

  • Python
    from math import prod
from gmpy2 import digits
def A382721(n): return prod(int(d,11)+1 for d in digits(n,11)) # Chai Wah Wu, Aug 10 2025

A382722 Number of entries in the n-th row of Pascal's triangle not divisible by 13.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 7, 14, 21
Offset: 0

Views

Author

N. J. A. Sloane, Apr 23 2025

Keywords

Links

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382721.

Programs

  • Python
    from math import prod
from gmpy2 import digits
def A382722(n): return prod(int(d,13)+1 for d in digits(n,13)) # Chai Wah Wu, Aug 10 2025

A387051 Number of entries in the n-th row of Pascal's triangle not divisible by 32.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 17, 34, 27, 36, 29, 38, 35, 40, 33, 42, 39, 44, 41, 46, 45, 48, 41, 50, 47, 52, 49, 54, 53, 56, 53, 58, 57, 60, 59, 62, 62, 64, 17, 34, 43, 68
Offset: 0

Views

Author

Chai Wah Wu, Aug 15 2025

Keywords

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382725, A386952, A387050.

Programs

  • Python
    def A387051(n):
    n1 = n>>1
    n2 = n1>>1
    n3 = n2>>1
    n4 = n3>>1
    np = ~n
    n10, n100, n110 = (k1:=n1&np).bit_count(), (k2:=(k1>>1)&np).bit_count(), (k3:=n2&k1).bit_count()
    n1100, n1000, n1010, n1110 = (k5:=n3&k2).bit_count(), (k4:=(k2>>1)&np).bit_count(), (k6:=(k1>>2)&k1).bit_count(), (k7:=n3&k3).bit_count()
    n10000, n11000, n10100, n11100 = ((k4>>1)&np).bit_count(), (n4&k4).bit_count(), ((k6>>1)&np).bit_count(), (n4&k5).bit_count()
    n10010, n11010, n10110, n11110 = ((k2>>2)&k1).bit_count(), (n4&k6).bit_count(), ((k1>>3)&k3).bit_count(), (n4&k7).bit_count()
    c = n10*(n10*(n10*(n10+2)+((n100<<2)+n110)*12+35)+((((((n1000<<2)+n1010+n1100<<1)+n100<<1)+n1110<<1)+n110)*12+154))//24
    c += n100*((n100<<1)+n110+1<<2)+(((n10000<<2)+n1000+n10010+n10100+n11000+1<<2)+n10110+n11010+n11100<<2)+n1110+n11110+(n110*(n110+5)>>1)
    return c<>4

A382724 Number of entries in the n-th row of Pascal's triangle not divisible by 6.

Original entry on oeis.org

1, 2, 3, 4, 4, 6, 5, 8, 9, 4, 6, 8, 6, 10, 14, 16, 12, 18, 5, 10, 11, 12, 16, 22, 11, 20, 27, 16, 10, 18, 18, 32, 12, 8, 14, 18, 6, 12, 16, 20, 18, 26, 18, 30, 36, 18, 24, 38, 14, 28, 38, 28, 38, 54, 17, 34, 15, 20, 26, 40, 23, 42, 45, 64, 12, 18, 14, 26, 36, 24, 38, 54, 11, 20, 29, 28, 38, 56, 37, 64, 81
Offset: 0

Views

Author

N. J. A. Sloane, Apr 23 2025

Keywords

Links

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382725.

A382726 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 7.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 28, 30, 34, 40, 48, 58, 70, 84, 87, 93, 102, 114, 129, 147, 168, 172, 180, 192, 208, 228, 252, 280, 285, 295, 310, 330, 355, 385, 420, 426, 438, 456, 480, 510, 546, 588, 595, 609, 630, 658, 693, 735, 784, 786, 790, 796, 804, 814, 826, 840, 844, 852, 864, 880, 900, 924, 952, 958, 970, 988, 1012, 1042, 1078
Offset: 0

Views

Author

N. J. A. Sloane, Apr 23 2025

Keywords

Comments

Partial sums of A382720. - James C. McMahon, Aug 15 2025

Links

Crossrefs

Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382731.

Programs

  • Mathematica
    a[n_]:=(n^2+3n+2)/2-Count[Mod[Flatten[Table[Binomial[m, k], {m, 0,n}, {k, 0,m}]] ,7],0];Array[a,69,0] (* James C. McMahon, Aug 15 2025 *)
  • Python
    from math import prod
from gmpy2 import digits
def A382726(n): return sum(prod(int(d)+1 for d in digits(m,7)) for m in range(n+1)) # Chai Wah Wu, Aug 10 2025
  • Python
    from math import prod
from gmpy2 import digits
def A382726(n):
    d = list(map(lambda x:int(x)+1,digits(n+1,7)[::-1]))
    return sum((b-1)*prod(d[a:])*28**a for a, b in enumerate(d))>>1 # Chai Wah Wu, Aug 13 2025

A382730 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 6.

Original entry on oeis.org

1, 3, 6, 10, 14, 20, 25, 33, 42, 46, 52, 60, 66, 76, 90, 106, 118, 136, 141, 151, 162, 174, 190, 212, 223, 243, 270, 286, 296, 314, 332, 364, 376, 384, 398, 416, 422, 434, 450, 470, 488, 514, 532, 562, 598, 616, 640, 678, 692, 720, 758, 786, 824, 878, 895, 929, 944, 964, 990, 1030, 1053, 1095, 1140, 1204, 1216, 1234, 1248, 1274
Offset: 0

Views

Author

N. J. A. Sloane, Apr 23 2025

Keywords

Links

Crossrefs

Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382731.
Showing 1-10 of 18 results. Next

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

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