A374175 - OEIS

%I #10 Jul 08 2024 09:46:20

%S 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,

%T 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,

%U 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

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

%C 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.

%H Hugo Pfoertner, <a href="/A374175/b374175.txt">Table of n, a(n) for n = 1..10000</a>

%F a(0) = oo.

%e Some observed positions of n in A373330:

%e       n   positions

%e      41   6         (A000217(6^2)=666, next smaller square = 625, 41 = 666 - 625)

%e       1   2     5

%e       9   3    10

%e      15   4   136

%e     ...

%e   25281 197  1590  22373

%e  264196 725 65684 276532.

%e No other terms = 3 or greater are known.

%o (PARI)

%o a373330(n) = {my(T=(n^4+n^2)/2); T-sqrtint(T)^2};

%o a374175(nmax,slimit) = {my(hits=vectorsmall(nmax)); for (k=0, slimit, my (j = a373330(k)); if(j>0 && j<=nmax, hits[j]++)); hits};

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

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Jun 30 2024