A075403 -id:A075403 - cp's OEIS frontend

A075402 Smallest number such that a(n) + T(n) is a prime, where T(n) is the n-th triangular number.

1, 0, 1, 1, 2, 2, 1, 1, 2, 4, 1, 1, 6, 2, 7, 1, 4, 2, 1, 1, 2, 4, 1, 7, 6, 2, 1, 3, 4, 2, 3, 13, 2, 4, 1, 7, 6, 2, 7, 1, 2, 4, 1, 1, 4, 6, 1, 5, 4, 2, 1, 3, 2, 2, 3, 1, 4, 10, 7, 1, 10, 20, 1, 1, 8, 2, 3, 1, 2, 18, 1, 5, 6, 2, 1, 1, 8, 2, 3, 11, 2, 4, 5, 1, 4, 20, 5, 1, 2, 4, 15, 5, 2, 16, 1, 1, 6, 10, 1

Offset: 1

Amarnath Murthy, Sep 23 2002

nonn

0 occurs only once in this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A075403.

If[PrimeQ[#],#,NextPrime[#]]-#&/@Accumulate[Range[100]] (* Harvey P. Dale, Nov 21 2012 *)

for(n=1,100,a=n*(n+1)/2:print1(nextprime(a)-a","))

Corrected and extended by Ralf Stephan, Mar 19 2003

A309877 a(n) is the smallest number k such that the difference between the next prime greater than k and k equals n.

Original entry on oeis.org

1, 0, 8, 7, 24, 23, 90, 89, 118, 117, 116, 115, 114, 113, 526, 525, 524, 523, 888, 887, 1130, 1129, 1338, 1337, 1336, 1335, 1334, 1333, 1332, 1331, 1330, 1329, 1328, 1327, 9552, 9551, 15690, 15689, 15688, 15687, 15686, 15685, 15684, 15683, 19616, 19615, 19614, 19613, 19612, 19611

Offset: 1

Ilya Gutkovskiy, Aug 21 2019

nonn

			+------+------+-----+
| a(n) | next | gap |
|      | prime|     |
+------+------+-----+
|   1  |   2  |  1  |
|   0  |   2  |  2  |
|   8  |  11  |  3  |
|   7  |  11  |  4  |
|  24  |  29  |  5  |
|  23  |  29  |  6  |
|  90  |  97  |  7  |
|  89  |  97  |  8  |
+------+------+-----+

Robert Israel, Table of n, a(n) for n = 1..282

Cf. A000101, A000230, A007918, A007920, A013632, A051652, A075403, A077019, A151800.

N:= 100:
A:= Vector(N,-1):
count:= 0: lastp:= 0:
while count < N do
  p:= nextprime(lastp);
  newvals:= select(t -> A[t]=-1, [$1..min(p-lastp,N)]);
  count:= count+nops(newvals);
  for k in newvals do A[k]:= p-k od;
  lastp:= p;
od:
convert(A,list); # Robert Israel, Aug 23 2019

Table[SelectFirst[Range[0, 20000], NextPrime[#] - # == n &], {n, 1, 50}]
Module[{nn=20000,d},d=Table[{n,NextPrime[n]-n},{n,0,nn}];Table[SelectFirst[d,#[[2]]==k&],{k,50}]][[;;,1]] (* Harvey P. Dale, Mar 23 2025 *)

a(n) = my(k=0); while(nextprime(k+1) - k != n, k++); k; \\ Michel Marcus, Aug 21 2019

a(n) = min {k : A013632(k) = n}.

cp's OEIS Frontend

A075402 Smallest number such that a(n) + T(n) is a prime, where T(n) is the n-th triangular number.

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