A071750 -id:A071750 - cp's OEIS frontend

A243935 Numbers m such that 5 divides A000041(m).

4, 7, 9, 14, 18, 19, 23, 24, 27, 29, 34, 38, 39, 44, 49, 54, 58, 59, 61, 64, 66, 68, 69, 71, 74, 79, 82, 84, 89, 94, 97, 99, 103, 104, 109, 114, 119, 120, 124, 127, 128, 129, 130, 134, 136, 139, 140, 142, 144, 149, 154, 159, 163, 164, 165, 169, 170, 173, 174

Offset: 1

Bruno Berselli, Jun 15 2014

Bruno Berselli, Table of n, a(n) for n = 1..1000

Numbers m such that k divides A000041(m), where k is prime: A001560 (k=2), A083214 (k=3), this sequence (k=5), A243936 (k=7), A027827 (k=11), A071750 (k=13). For k composite: A237278 (k=4), A035700 (k=12).

[n: n in [1..200] | IsZero(NumberOfPartitions(n) mod 5)];

Select[Range[200], Mod[PartitionsP[#], 5] == 0 &]

is(n)=numbpart(n)%5==0 \\ Charles R Greathouse IV, Apr 08 2015

# From Peter Luschny in A000041
@CachedFunction
def A000041(n):
    if n == 0: return 1
    S = 0; J = n-1; k = 2
    while 0 <= J:
        T = A000041(J)
        S = S+T if is_odd(k//2) else S-T
        J -= k if is_odd(k) else k//2
        k += 1
    return S
[n for n in (0..200) if mod(A000041(n),5) == 0]

A243936 Numbers m such that 7 divides A000041(m).

Original entry on oeis.org

5, 10, 11, 12, 16, 18, 19, 24, 26, 27, 33, 37, 39, 40, 41, 47, 48, 52, 53, 54, 55, 61, 68, 75, 76, 82, 83, 89, 96, 97, 103, 110, 111, 117, 124, 125, 131, 138, 140, 145, 147, 152, 159, 166, 170, 173, 177, 180, 187, 191, 194, 201, 208, 213, 215, 222, 225, 229, 232

Offset: 1

Bruno Berselli, Jun 15 2014

Bruno Berselli, Table of n, a(n) for n = 1..1000

Numbers m such that k divides A000041(m), where k is prime: A001560 (k=2), A083214 (k=3), A243935 (k=5), this sequence (k=7), A027827 (k=11), A071750 (k=13). For k composite: A237278 (k=4), A035700 (k=12).

[n: n in [1..250] | IsZero(NumberOfPartitions(n) mod 7)];

Select[Range[250], Mod[PartitionsP[#], 7] == 0 &]

is(n)=numbpart(n)%7==0 \\ Charles R Greathouse IV, Apr 08 2015

# From Peter Luschny in A000041
@CachedFunction
def A000041(n):
    if n == 0: return 1
    S = 0; J = n-1; k = 2
    while 0 <= J:
        T = A000041(J)
        S = S+T if is_odd(k//2) else S-T
        J -= k if is_odd(k) else k//2
        k += 1
    return S
[n for n in (0..250) if mod(A000041(n),7) == 0]

cp's OEIS Frontend

A243935 Numbers m such that 5 divides A000041(m).

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