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.

User: FUNG Cheok Yin

FUNG Cheok Yin's wiki page.

FUNG Cheok Yin has authored 17 sequences. Here are the ten most recent ones:

A289500 Number of primes in the interval [9n, 10n].

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 4, 2, 1, 4, 3, 3, 3, 4, 3, 5, 4, 2, 4, 5, 5, 4, 4, 5, 6, 5, 4, 5, 4, 6, 5, 6, 6, 7, 7, 6, 7, 7, 6, 8, 8, 8, 9, 9, 8, 8, 9, 6, 8, 7, 7, 6, 7, 8, 8, 10, 10, 12, 11, 10, 12, 12, 11, 12, 10, 11, 12, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 12 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289498, A289499.
Cf. A038801.

Programs

  • Magma
    [0] cat [#PrimesInInterval(9*n, 10*n): n in [2..100]]; // Vincenzo Librandi, Jul 13 2017
  • Maple
    seq(numtheory:-pi(10*n)-numtheory:-pi(9*n),n=1..100); # Robert Israel, Jul 12 2017
  • Mathematica
    Join[{0}, Table[PrimePi[10 n] - PrimePi[9 n], {n, 2, 100}]] (* Vincenzo Librandi, Jul 13 2017 *)
  • PARI
    a(n) = primepi(10*n) - primepi(9*n); \\ Michel Marcus, Jul 12 2017

Formula

a(n) = n/log(n) + (1 + log(3^18/10^10))*n/log(n)^2 + O(n/log(n)^3) as n -> infinity. - Robert Israel, Jul 12 2017

A289499 Number of primes in the interval [8n, 9n].

Original entry on oeis.org

0, 1, 0, 0, 2, 1, 2, 2, 2, 2, 2, 4, 3, 1, 2, 3, 4, 3, 3, 4, 3, 5, 4, 4, 2, 5, 6, 6, 5, 5, 6, 7, 6, 4, 6, 5, 5, 6, 6, 6, 7, 7, 8, 7, 7, 7, 8, 7, 8, 9, 9, 11, 9, 9, 9, 10, 10, 8, 8, 7, 8, 8, 7, 8, 9, 9, 11, 11, 13, 12, 12, 13, 13, 14, 13, 13, 13, 12, 12, 13
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289498, A289500.

A289498 Number of primes in the interval [7n, 8n].

Original entry on oeis.org

1, 0, 1, 2, 1, 2, 1, 2, 2, 3, 2, 1, 3, 4, 3, 2, 2, 4, 4, 3, 5, 4, 5, 4, 6, 4, 5, 4, 4, 6, 6, 6, 6, 7, 6, 7, 7, 6, 6, 7, 5, 5, 6, 7, 7, 7, 8, 9, 9, 8, 8, 8, 9, 9, 9, 9, 9, 11, 11, 11, 11, 10, 11, 11, 10, 10, 8, 9, 9, 9, 9, 9, 9, 10, 10, 12, 13, 14, 14, 13
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289499, A289500.

A289497 Number of primes in the interval [6n, 7n].

Original entry on oeis.org

1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 5, 4, 2, 2, 4, 4, 4, 4, 5, 5, 6, 5, 5, 6, 5, 5, 5, 5, 5, 7, 7, 8, 7, 7, 7, 8, 8, 7, 7, 8, 8, 6, 6, 6, 8, 9, 8, 7, 8, 10, 10, 10, 10, 9, 9, 10, 11, 11, 10, 10, 12, 12, 12, 12, 12, 12, 13, 13, 11, 12, 12, 10, 9, 10, 10
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289496, A289498, A289499, A289500.

Programs

  • PARI
    a(n) = primepi(7*n) - primepi(6*n); \\ Michel Marcus, Jul 08 2017

A289496 Number of primes in the interval [5n, 6n].

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 3, 3, 4, 3, 2, 3, 4, 6, 5, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 6, 6, 5, 7, 7, 6, 7, 8, 8, 9, 9, 8, 9, 9, 9, 9, 8, 9, 10, 9, 8, 8, 7, 8, 9, 10, 10, 10, 9, 10, 11, 11, 12, 11, 12, 11, 11, 11, 12, 13, 13, 12, 13, 14, 14, 14
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289495, A289497, A289498, A289499, A289500.

Programs

A289495 Number of primes in the interval [4n, 5n].

Original entry on oeis.org

1, 0, 1, 2, 1, 1, 2, 1, 3, 3, 2, 2, 3, 3, 4, 4, 4, 4, 3, 3, 4, 6, 6, 6, 5, 4, 4, 5, 4, 5, 6, 6, 6, 7, 6, 7, 8, 6, 8, 9, 8, 7, 8, 7, 7, 8, 9, 9, 9, 7, 8, 9, 9, 10, 11, 11, 12, 11, 11, 10, 9, 10, 11, 12, 11, 10, 11, 10, 10, 11, 10, 11, 11, 11, 12
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289494, A289496, A289497, A289498, A289499, A289500.

Programs

  • PARI
    a(n) = primepi(5*n) - primepi(4*n); \\ Michel Marcus, Jul 08 2017

A289494 Number of primes in the interval [3n, 4n].

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 3, 4, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 4, 4, 6, 6, 6, 7, 6, 6, 7, 7, 6, 7, 6, 5, 6, 6, 7, 8, 9, 8, 8, 9, 9, 8, 9, 10, 11, 10, 10, 10, 10, 9, 9, 10, 10, 11, 11, 11, 11, 12, 11, 11, 11, 10, 12, 12, 13, 14, 14, 14, 15, 14
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289493, A289495, A289496, A289497, A289498, A289499, A289500.

Programs

  • Mathematica
    Join[{1},Rest[Table[PrimePi[4n]-PrimePi[3n],{n,80}]]] (* Harvey P. Dale, Dec 30 2024 *)

A289493 Number of primes in the interval [2n, 3n].

Original entry on oeis.org

2, 1, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 3, 4, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 6, 6, 6, 7, 7, 7, 6, 6, 7, 7, 8, 8, 8, 9, 9, 8, 8, 7, 8, 9, 8, 9, 10, 10, 9, 10, 10, 9, 10, 9, 9, 10, 9, 10, 10, 11, 12, 12, 12, 12, 13, 13, 14, 14, 13, 12, 13, 13, 13, 13, 13, 13, 14, 15, 14, 15
Offset: 1

Views

Author

FUNG Cheok Yin, Jul 07 2017

Keywords

Links

Crossrefs

Cf. A035250, A289494, A289495, A289496, A289497, A289498, A289499, A289500.
Cf. A000720 (PrimePi), A101985 (numbers occurring here exactly once).

Programs

Formula

a(n) = A000720(3n) - A000720(2n), for n > 1. - M. F. Hasler, Sep 29 2019

A283209 Primes of the form 299...977...7 with at least one 9 and one 7.

Original entry on oeis.org

299777, 299977, 29999777, 299999977, 2999999777, 299999999777, 2999977777777, 299999999999977, 2999999999977777777, 2999999999999999977, 299999999999977777777, 299999999999999999977, 2999999999999999777777
Offset: 1

Views

Author

FUNG Cheok Yin, Mar 03 2017

Keywords

Comments

If the number of 7's modulo 3 equals 1, the corresponding 29..97..7 term cannot be in sequence because it is divisible by 3.
If the number of 9's modulo 6 equals 5, the corresponding 29..97..7 term cannot be in sequence because 299999 and 999999 are divisible by 7.
If the number of 7's and the number of 9's are both odd, the corresponding 29..97..7 term cannot be in sequence because it is divisible by 11.

Links

Programs

  • Mathematica
    Sort@ Select[Map[FromDigits@ Join[{2}, ConstantArray[9, #1], ConstantArray[7, #2]] & @@ # &, Select[Tuples[Range@ 20, 2], Times @@ Boole@ Map[OddQ, #] == 0 &]], PrimeQ] (* Michael De Vlieger, Mar 06 2017 *)
  • PARI
    do(n)=my(v=List(),p=29,q); for(d=3,n, p=10*p+7; q=p; forstep(i=d-3,1,-1, if(ispseudoprime(q+=2*10^i), listput(v,q)))); Vec(v) \\ Charles R Greathouse IV, Mar 06 2017

Extensions

More terms from Charles R Greathouse IV, Mar 06 2017

A283161 Natural numbers whose digits can be formed by typing non-adjacent keys on a 123-456-789 keypad without repeating a digit.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 15, 16, 17, 18, 19, 24, 26, 27, 28, 29, 31, 34, 35, 37, 38, 39, 42, 43, 46, 48, 49, 51, 53, 57, 59, 61, 62, 64, 67, 68, 71, 72, 73, 75, 76, 79, 81, 82, 83, 84, 86, 91, 92, 93, 94, 95, 97, 135, 137, 138, 139, 153, 157, 159, 167, 168, 173, 175, 176, 179, 183, 186, 193, 195
Offset: 1

Views

Author

FUNG Cheok Yin, Mar 02 2017

Keywords

Comments

Or say numbers which are "very difficult" to be typed on a keypad without the zero. (See description of A215009.)

Examples

			The keypad is:
+-----+
|1|2|3|
+-+-+-+
|4|5|6|
+-+-+-+
|7|8|9|
+-+-+-+
It is visibly obvious that 168 can be formed on the keypad, and each pairwise digits of 168 are not adjacent.

Links

Crossrefs

Cf. A280593, A215009, A006506(3)

Programs

  • Mathematica
    no = IntegerDigits @ {12,14,23,25,34,36,45,47,56,58,69,78,89}; Sort[ FromDigits /@ Flatten[ Permutations /@ Select[ Subsets[ Range@ 9, {1, 9}], Intersection[ Subsets[#, {2}], no] == {} &], 1]] (* Giovanni Resta, Apr 06 2017 *)

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