A243111 Difference between the smallest triangular number >= n-th prime and the n-th prime.

1, 0, 1, 3, 4, 2, 4, 2, 5, 7, 5, 8, 4, 2, 8, 2, 7, 5, 11, 7, 5, 12, 8, 2, 8, 4, 2, 13, 11, 7, 9, 5, 16, 14, 4, 2, 14, 8, 4, 17, 11, 9, 19, 17, 13, 11, 20, 8, 4, 2, 20, 14, 12, 2, 19, 13, 7, 5, 23, 19, 17, 7, 18, 14, 12, 8, 20, 14, 4, 2, 25, 19, 11, 5, 27, 23, 17, 9, 5, 26, 16, 14, 4, 2, 26

Offset

1,4

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

   x,   0  ,   x  ,     x  ,         x
  0 0  0 0    0 0      x x          x x
             0 0 0    0 0 0        0 0 x
                     0 0 0 0      0 0 0 0
                                 0 0 0 0 0
prime(n) = 2,3,5,7,11,...
x -> we need respectively 1, 0, 1, 3 and 4 numbers to complete the whole triangle.

Mathematica

Module[{upto=100, tnos}, tnos=Accumulate[Range[Ceiling[(Sqrt[8*Prime[upto]+ 1]- 1)/2]]]; Table[SelectFirst[tnos, #>=Prime[n]&]-Prime[n], {n, upto}]] (* Harvey P. Dale, Jan 15 2015 *)

Prog

(PARI)
a(n)=k=1; while(k*(k+1)/2<prime(n), k++); return(k*(k+1)/2-prime(n))
vector(100, n, a(n)) \\ Derek Orr, Aug 21 2014

Crossrefs

Cf. A000040, A002262, A000217.

Sequence in context: A326044 A011414 A155746 * A084511 A084521 A214923

Adjacent sequences: A243108 A243109 A243110 * A243112 A243113 A243114

Keyword

nonn,easy

Author

Odimar Fabeny, Aug 20 2014

Status

approved