A374175 a(n) is the conjectured number of occurrences of n in A373330.

2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Hugo Pfoertner, Jun 30 2024

Keywords

• nonn

Comments

The sequence must be considered as conjectural, since so far no proof is known for the non-occurrence of arbitrarily small terms > 0 for very large n in A373330, despite the growing distance reserve observed in A373331 and A373332.

Examples

			Some observed positions of n in A373330:
      n   positions
     41   6         (A000217(6^2)=666, next smaller square = 625, 41 = 666 - 625)
      1   2     5
      9   3    10
     15   4   136
    ...
  25281 197  1590  22373
 264196 725 65684 276532.
No other terms = 3 or greater are known.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A373330, A373333 (positions of terms > 0).

Programs

PARI

a373330(n) = {my(T=(n^4+n^2)/2); T-sqrtint(T)^2};
a374175(nmax,slimit) = {my(hits=vectorsmall(nmax)); for (k=0, slimit, my (j = a373330(k)); if(j>0 && j<=nmax, hits[j]++)); hits};

Formula

a(0) = oo.