A272879 -id:A272879 - cp's OEIS frontend

A272314 Number of representations of A067128(n), n>=2, as sum A067128(k)+A067128(t), k<=t, or a(n)=0 if there is no such expression.

1, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 6, 4, 5, 3, 2, 3, 3, 3, 3, 4, 5, 2, 5, 4, 7, 7, 5, 5, 4, 4, 3, 4, 2, 2, 3, 4, 4, 4, 5, 8, 3, 3, 3, 3, 3, 4, 3, 4, 3, 5, 4, 4, 3, 5, 7, 4, 6, 3, 8, 6, 8, 6, 6, 6, 3, 4, 4, 4, 4, 4, 5, 5, 4, 5, 4, 4, 4, 6

Offset: 2

Vladimir Shevelev, May 10 2016

nonn

The first zero terms calculated by Peter J. C. Moses appear for n=163,186,248,...

Peter J. C. Moses, Table of n, a(n) for n = 2..3001

Cf. A067128, A272879, A272901.

More terms from Peter J. C. Moses, May 10 2016

A272901 Smallest k>=1 such that A067128(n+k) - A067128(n) is in A067128 or a(n)=0 if there is no such k.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, May 09 2016

nonn

For n=151, the required k, if it exists, should be >9800. So one can conjecture that a(151) is the first zero term.

Cf. A067128, A272879.

A272901 := proc(n)
    local k;
    for k from 1 do
        if isA067128(A067128(n+k)-A067128(n)) then
            return k;
        end if;
    end do:
end proc:
for n from 1 do
    printf("%d %d\n",n,A272901(n)) ;
end do: # R. J. Mathar, Apr 15 2024

cp's OEIS Frontend

A272314 Number of representations of A067128(n), n>=2, as sum A067128(k)+A067128(t), k<=t, or a(n)=0 if there is no such expression.

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