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.

Previous Showing 11-15 of 15 results.

A337572 Numbers having at least one 4 in their representation in base 5.

Original entry on oeis.org

4, 9, 14, 19, 20, 21, 22, 23, 24, 29, 34, 39, 44, 45, 46, 47, 48, 49, 54, 59, 64, 69, 70, 71, 72, 73, 74, 79, 84, 89, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 129, 134
Offset: 1

Views

Author

François Marques, Sep 19 2020

Keywords

Comments

Complementary sequence to A020654.

Examples

			75 is not in the sequence since it is 300_5 in base 5, but 74 is in the sequence since it is 244_5 in base 5.

Links

Crossrefs

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), this sequence (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Maple
    seq(`if`(numboccur(4, convert(n, base, 5))>0, n, NULL), n=0..100);
  • Mathematica
    Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 5 ], 4 ]>0)& ]
  • PARI
    isok(m) = #select(x->(x==4), digits(m, 5)) >= 1; \\ Michel Marcus, Sep 20 2020
  • Python
    from gmpy2 import digits
def A337572(n):
    def f(x):
        l = (s:=digits(x,5)).find('4')
        if l >= 0: s = s[:l]+'3'*(len(s)-l)
        return n+int(s,4)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A333656 Numbers having at least one 5 in their representation in base 6.

Original entry on oeis.org

5, 11, 17, 23, 29, 30, 31, 32, 33, 34, 35, 41, 47, 53, 59, 65, 66, 67, 68, 69, 70, 71, 77, 83, 89, 95, 101, 102, 103, 104, 105, 106, 107, 113, 119, 125, 131, 137, 138, 139, 140, 141, 142, 143, 149, 155, 161, 167, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184
Offset: 1

Views

Author

François Marques, Sep 20 2020

Keywords

Comments

Complementary sequence to A037465.

Examples

			22 is not in the sequence since it is 34_6 in base 6, but 23 is in the sequence since it is 35_6 in base 6.

Links

Crossrefs

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), this sequence (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Maple
    seq(`if`(numboccur(5, convert(n, base, 6))>0, n, NULL), n=0..100);
  • Mathematica
    Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 6 ], 5 ]>0)& ]
  • PARI
    isok(m) = #select(x->(x==5), digits(m, 6)) >= 1;
  • Python
    from gmpy2 import digits
def A333656(n):
    def f(x):
        l = (s:=digits(x,6)).find('5')
        if l >= 0: s = s[:l]+'4'*(len(s)-l)
        return n+int(s,5)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A337141 Numbers having at least one 6 in their representation in base 7.

Original entry on oeis.org

6, 13, 20, 27, 34, 41, 42, 43, 44, 45, 46, 47, 48, 55, 62, 69, 76, 83, 90, 91, 92, 93, 94, 95, 96, 97, 104, 111, 118, 125, 132, 139, 140, 141, 142, 143, 144, 145, 146, 153, 160, 167, 174, 181, 188, 189, 190, 191, 192, 193, 194, 195, 202, 209, 216, 223, 230, 237, 238, 239, 240
Offset: 1

Views

Author

François Marques, Sep 20 2020

Keywords

Comments

Complementary sequence to A020657.

Examples

			33 is not in the sequence since it is 45_7 in base 7, but 34 is in the sequence since it is 46_7 in base 7.

Links

Crossrefs

Cf. Numbers with at least one digit b-1 in base b: A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), this sequence (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Maple
    seq(`if`(numboccur(6, convert(n, base, 7))>0, n, NULL), n=0..100);
  • Mathematica
    Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 7 ], 6 ]>0)& ]
Select[Range[300],DigitCount[#,7,6]>0&] (* Harvey P. Dale, Dec 23 2020 *)
  • PARI
    isok(m) = #select(x->(x==6), digits(m, 7)) >= 1;
  • Python
    from gmpy2 import digits
def A337141(n):
    def f(x):
        l = (s:=digits(x,7)).find('6')
        if l >= 0: s = s[:l]+'5'*(len(s)-l)
        return n+int(s,6)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A337239 Numbers having at least one 7 in their representation in base 8.

Original entry on oeis.org

7, 15, 23, 31, 39, 47, 55, 56, 57, 58, 59, 60, 61, 62, 63, 71, 79, 87, 95, 103, 111, 119, 120, 121, 122, 123, 124, 125, 126, 127, 135, 143, 151, 159, 167, 175, 183, 184, 185, 186, 187, 188, 189, 190, 191, 199, 207, 215, 223, 231, 239, 247, 248, 249, 250, 251, 252, 253, 254, 255
Offset: 1

Views

Author

François Marques, Sep 20 2020

Keywords

Comments

Complementary sequence to A037474.

Examples

			54 is not in the sequence since it is 66_8 in base 8, but 55 is in the sequence since it is 67_8 in base 8.

Links

Crossrefs

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), this sequence (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

  • Maple
    seq(`if`(numboccur(7, convert(n, base, 8))>0, n, NULL), n=0..100);
  • Mathematica
    Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 8 ], 7 ]>0)& ]
  • PARI
    isok(m) = #select(x->(x==7), digits(m, 8)) >= 1;
  • Python
    def A337239(n):
    def f(x):
        s = oct(x)[2:]
        l = s.find('7')
        if l >= 0:
            s = s[:l]+'6'*(len(s)-l)
        return n+int(s,7)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A031216 Write primes in base 10 but interpret as if in base 11.

Original entry on oeis.org

2, 3, 5, 7, 12, 14, 18, 20, 25, 31, 34, 40, 45, 47, 51, 58, 64, 67, 73, 78, 80, 86, 91, 97, 106, 122, 124, 128, 130, 135, 150, 155, 161, 163, 174, 177, 183, 190, 194, 201, 207, 210, 221, 223, 227, 229, 254, 267, 271, 273, 278, 284, 287, 298, 304, 311
Offset: 1

Views

Author

Jeff Burch

Keywords

Examples

			13_10 = 11+2 -> 12_11, so 5th term is 12.

Links

Crossrefs

Cf. A000040, A171397.

Programs

  • Maple
    a:= n-> (l-> add(l[i]*11^(i-1), i=1..nops(l)))(convert(ithprime(n),base,10)):
seq(a(n), n=1..56);  # Alois P. Heinz, Aug 30 2024
  • PARI
    a(n) = fromdigits(digits(prime(n)), 11); \\ Michel Marcus, Aug 31 2024
  • Python
    from sympy import prime
def A031216(n): return int(str(prime(n)),11) # Chai Wah Wu, Aug 30 2024

Formula

a(n) = A171397(prime(n)). - Michel Marcus, Aug 31 2024

Extensions

a(25) corrected by Sean A. Irvine, Apr 16 2020
Previous Showing 11-15 of 15 results.

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