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: Kei Ryan

Kei Ryan's wiki page.

Kei Ryan has authored 6 sequences.

A308375 Digital sum of composite numbers.

Original entry on oeis.org

4, 6, 8, 9, 1, 3, 5, 6, 7, 9, 2, 3, 4, 6, 7, 8, 9, 10, 3, 5, 6, 7, 8, 9, 11, 12, 4, 6, 8, 9, 10, 12, 13, 5, 6, 7, 9, 10, 11, 12, 13, 6, 8, 9, 10, 11, 12, 14, 15, 7, 9, 11, 12, 13, 14, 15, 8, 9, 10, 12, 13, 14, 15, 16, 9, 10, 11, 12, 13, 14, 15, 17, 18, 1, 3, 5
Offset: 1

Views

Author

Kei Ryan, May 27 2019

Keywords

Examples

			The 6th term is 3 because the digital sum of 12 (the 6th composite number) is 3 (1+2).

Crossrefs

Cf. A002808 (composite numbers), A007953 (sum of digits).
Cf. A007605 (sum of digits of primes).

Programs

  • Mathematica
    Total /@ IntegerDigits /@ Select[Range[104], CompositeQ] (* Giovanni Resta, May 28 2019 *)
  • PARI
    lista(nn) = forcomposite(n=1, nn, print1(sumdigits(n), ", ")); \\ Michel Marcus, May 28 2019

Formula

a(n) = A007953(A002808(n)).

A322062 Sums of pairs of consecutive terms of Pascal's triangle read by row.

Original entry on oeis.org

2, 2, 2, 3, 3, 2, 4, 6, 4, 2, 5, 10, 10, 5, 2, 6, 15, 20, 15, 6, 2, 7, 21, 35, 35, 21, 7, 2, 8, 28, 56, 70, 56, 28, 8, 2, 9, 36, 84, 126, 126, 84, 36, 9, 2, 10, 45, 120, 210, 252, 210, 120, 45, 10, 2, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 2, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1
Offset: 0

Views

Author

Kei Ryan, Nov 25 2018

Keywords

Comments

Sums of pairs of adjacent terms of A007318. - N. J. A. Sloane, Jan 27 2019

Examples

			The 8th term is 6 because it is the sum of the 8th and 9th terms of Pascal's triangle read by row (3 + 3).
Triangle begins:
  2;
  2,  2;
  3,  3,  2;
  4,  6,  4,  2;
  5, 10, 10,  5,  2;
  ...

Crossrefs

Cf. A007318, A168557.

Programs

  • Mathematica
    v = Flatten[Table[Binomial[n, k], {n, 0, 10}, {k, 0, n}]]; Most[v] + Rest[v] (* Amiram Eldar, Nov 25 2018 *)
  • PARI
    T(n, k) = if (kMichel Marcus, Nov 25 2018

Formula

T(n, k) = if (kMichel Marcus, Nov 25 2018

A321789 Factorials of terms of Pascal's triangle by row.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 24, 720, 24, 1, 1, 120, 3628800, 3628800, 120, 1, 1, 720, 1307674368000, 2432902008176640000, 1307674368000, 720, 1, 1, 5040, 51090942171709440000, 10333147966386144929666651337523200000000, 10333147966386144929666651337523200000000, 51090942171709440000, 5040, 1
Offset: 1

Views

Author

Kei Ryan, Nov 19 2018

Keywords

Examples

			The 12th term is 24 because the 12th term of Pascal's triangle by row is 4 and 4! is 24 (4*3*2*1).

Crossrefs

Cf. A007318, A000142.

Programs

  • GAP
    Flat(List([0..7],n->List([0..n],k->Factorial(Binomial(n,k))))); # Muniru A Asiru, Dec 20 2018
  • Maple
    T:=(n,k)->factorial(binomial(n,k)): seq(seq(T(n,k),k=0..n),n=0..7); # Muniru A Asiru, Dec 20 2018
  • Mathematica
    Flatten[Table[Binomial[n, k]!, {n, 0, 6}, {k, 0, n}]] (* Amiram Eldar, Nov 19 2018 *)

A321663 a(n) = prime(n)^prime(n+2).

Original entry on oeis.org

32, 2187, 48828125, 96889010407, 505447028499293771, 1461920290375446110677, 19967568900859523802559065713, 12129821994589221844500501021364910179, 1635170022196481349560959748587682926364327, 1284475787728524720826927656893473276744000042113841709
Offset: 1

Views

Author

Kei Ryan, Nov 16 2018

Keywords

Examples

			a(3)=48828125 because 5 is the 3rd prime, 11 is the 5th prime and 5^11=48828125.

Crossrefs

Cf. A053089 (prime(n)^prime(n+1)), A000040.

Programs

  • Mathematica
    Array[Prime[#]^Prime[# + 2] &, 10] (* Michael De Vlieger, Nov 25 2018 *)
#[[1]]^#[[3]]&/@Partition[Prime[Range[20]],3,1] (* Harvey P. Dale, Jun 20 2023 *)

Formula

a(n) = prime(n)^prime(n+2).

A321741 Product of the first n terms of A007318 (Pascal), read as a sequence.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 2, 6, 18, 18, 18, 72, 432, 1728, 1728, 1728, 8640, 86400, 864000, 4320000, 4320000, 4320000, 25920000, 388800000, 7776000000, 116640000000, 699840000000, 699840000000, 699840000000, 4898880000000, 102876480000000, 3600676800000000, 126023688000000000, 2646497448000000000, 18525482136000000000, 18525482136000000000
Offset: 1

Views

Author

Kei Ryan, Nov 17 2018

Keywords

Examples

			The 10th term is 18 because the first 10 terms of Pascal's Triangle by row are 1,1,1,1,2,1,1,3,3,1 and 1*1*1*1*2*1*1*3*3*1=18.

Links

Crossrefs

Cf. A007318, A163866 (partial sums).

Programs

  • Mathematica
    FoldList[Times, 1, Rest[Flatten[Table[Binomial[n, k], {n, 0, 7}, {k, 0, n}]]]] (* Amiram Eldar, Nov 18 2018 *)
  • PARI
    lista(nn) = {my(i=0, j=0, p=1); for (n=1, nn, p *= binomial(i, j); print1(p, ", "); j++; if (j > i, j = 0; i++););} \\ Michel Marcus, Jan 25 2019

Formula

a(n) = Product_{j=0..n-1} P(n), where P(n) = A007318(n) (as a sequence). - Wolfdieter Lang, Jan 25 2019

A319675 Sum of digits of prime(n) and digits of prime(n+1).

Original entry on oeis.org

5, 8, 12, 9, 6, 12, 18, 15, 16, 15, 14, 15, 12, 18, 19, 22, 21, 20, 21, 18, 26, 27, 28, 33, 18, 6, 12, 18, 15, 15, 15, 16, 24, 27, 21, 20, 23, 24, 25, 28, 27, 21, 24, 30, 36, 23, 11, 18, 24, 21, 22, 21, 15, 22, 25, 28, 27, 26, 27, 24, 27, 24, 15, 12, 18, 18
Offset: 1

Views

Author

Kei Ryan, Sep 26 2018

Keywords

Examples

			For n=6 , a(6) is the sum of digits of 13 and 17 which is 12.

Crossrefs

Cf. A007605, A045533.

Programs

  • GAP
    P:=Filtered([1..400],IsPrime);; List(List([1..Size(P)-1],i->ListOfDigits(P[i])+ListOfDigits(P[i+1])),Sum); # Muniru A Asiru, Sep 26 2018
  • Magma
    [&+Intseq(NthPrime(n)) + &+Intseq(NthPrime(n+1)): n in [1..87]]; // Vincenzo Librandi, Sep 26 2018
  • Mathematica
    Table[Plus@@IntegerDigits[Prime[n]] + Plus@@IntegerDigits[Prime[n + 1]], {n, 80}] (* Vincenzo Librandi, Sep 26 2018 *)

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

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