login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A176653 Triangle, read by rows, defined by T(n, m) = f(n-m)*f(n) - f(n-0)*f(0) + 1, where f(n) is 1 if n = 0 and Prime(n) otherwise. 2
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 3, 4, 1, 1, 4, 5, 5, 4, 1, 1, 10, 9, 13, 9, 10, 1, 1, 10, 17, 19, 19, 17, 10, 1, 1, 16, 21, 37, 31, 37, 21, 16, 1, 1, 16, 29, 43, 55, 55, 43, 29, 16, 1, 1, 18, 29, 57, 63, 93, 63, 57, 29, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are: {1, 2, 4, 6, 13, 20, 53, 94, 181, 288, 429, ...}.

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

T(n, m) = f(n-m)*f(n) - f(n-0)*f(0) + 1, where f(n) is 1 if n = 0 and Prime(n) otherwise.

EXAMPLE

Triangle begins as:

  1;

  1,  1;

  1,  2,  1;

  1,  2,  2,  1;

  1,  4,  3,  4,  1;

  1,  4,  5,  5,  4,  1;

  1, 10,  9, 13,  9, 10,  1;

  1, 10, 17, 19, 19, 17, 10,  1;

  1, 16, 21, 37, 31, 37, 21, 16,  1;

  1, 16, 29, 43, 55, 55, 43, 29, 16,  1;

  1, 18, 29, 57, 63, 93, 63, 57, 29, 18, 1;

MATHEMATICA

f[n_]:= If[n==0, 1, Prime[n]]; T[n_, m_] = f[n-m]*f[m] - f[n]*f[0] + 1; Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, May 07 2019 *)

PROG

(PARI)

{f(n) = if(n==0, 1, prime(n))};

{T(n, k) = f(n-k)*f(k) - f(k) + 1};

for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, May 07 2019

(MAGMA)

f:= func< n | n eq 0 select 1 else NthPrime(n) >;

[[f(n-k)*f(k) - f(n) + 1: k in [0..n]]: n in [0..12]]; // G. C. Greubel, May 07 2019

(Sage)

def f(n):

    if (n==0): return 1

    else: return nth_prime(n)

def T(n, k): return f(n-k)*f(k) - f(n) +1

[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, May 07 2019

CROSSREFS

Cf. A146985

Sequence in context: A106476 A101566 A331447 * A174842 A156074 A051287

Adjacent sequences:  A176650 A176651 A176652 * A176654 A176655 A176656

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Apr 22 2010

EXTENSIONS

Edited by G. C. Greubel, May 07 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 01:01 EST 2020. Contains 338864 sequences. (Running on oeis4.)