Andrej Jakobcic - cp's OEIS frontend

A383430 a(n) is the size of the largest subset of {1,...,n} such that no two elements differ by 5 or 8.

1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 20, 20, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 29, 29, 30, 30, 30, 31, 32, 32, 33, 34, 34, 34, 35, 35, 35, 36

Offset: 1

Andrej Jakobcic, May 05 2025

			a(13) = 6 because {1, 2, 4, 5, 8, 11} is a 6-element subset of {1..13} which has no two elements differing by 5 or 8, and there is no larger subset that works.

Mathematics Stack Exchange, Find the maximum number of elements in the set M such that no two elements have a difference of 5 or 8
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Cf. A369149.

def a(n):
    low = [0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 9, 10, 10, 10]
    if n < len(low):
        return low[n]
    else:
        return a(n - 13) + 6

a(n) = a(n-13) + 6 for n > 20.

A380770 Number of letters in the Slovene name of n (feminine, nominative), excluding spaces.

Original entry on oeis.org

3, 3, 3, 3, 5, 3, 4, 5, 4, 5, 5, 6, 8, 8, 10, 8, 9, 10, 9, 10, 7, 12, 12, 12, 14, 12, 13, 14, 13, 14, 8, 13, 13, 13, 15, 13, 14, 15, 14, 15, 10, 15, 15, 15, 17, 15, 16, 17, 16, 17, 8, 13, 13, 13, 15, 13, 14, 15, 14, 15, 9, 14, 14, 14, 16, 14, 15, 16, 15, 16, 10, 15, 15, 15, 17, 15, 16, 17, 16, 17, 9, 14, 14, 14, 16, 14, 15, 16, 15

Offset: 0

Andrej Jakobcic, Feb 02 2025

Repeatedly applying the map k -> a(k) to any starting value n always leads to 3 = "tri".
There is difference in gender (nominative) for number 1 and number 2.
1 - en (m.), ena (f.), eno (n.)
2 - dva (m.), dve (f.), dve (n.)
and similar 101, 201, etc, ...
All other numbers have the same form for all genders.

			a(0)=3 [nič], a(1)=3 [ena], a(2)=3 [dve], a(3)=3 [tri], a(4)=5 [štiri]

ŠUSS, How do you spell 143800 in words? (in Slovenian).
Index entries for sequences related to number of letters in n

Cf. A005589.

from num2words import num2words
def a(n):
    return len(num2words(n, lang='sl').replace(' ', ''))
print([a(n) for n in range(1000)])

A380433 Numbers that are a sum of both four and six consecutive prime numbers.

Original entry on oeis.org

72, 660, 724, 1788, 1956, 3300, 3348, 3528, 4280, 4520, 4920, 5064, 5250, 7764, 8412, 8598, 9210, 9378, 9456, 9920, 10134, 10974, 11256, 12054, 12762, 13830, 14106, 14184, 14294, 14826, 18180, 18600, 18876, 19380, 19922, 20344, 20900, 21636, 21728, 22286, 22608

Offset: 1

Andrej Jakobcic, Jan 24 2025

nonn

All terms are even.

			72 = (13+17+19+23) = (5+7+11+13+17+19).

Intersection of A034963 and A127333.

A308708 Numbers k such that k^3 contains exactly three distinct digits; numbers with trailing zeros are excluded.

Original entry on oeis.org

5, 6, 8, 9, 14, 15, 36, 62, 92, 101, 173, 192, 211, 888, 1001, 3543, 10001, 100001, 110011, 146796, 1000001, 10000001, 100000001, 1000000001, 10000000001

Offset: 1

Andrej Jakobcic, Aug 01 2019

10^k + 1 (A000533(k)) is a term for k >= 2. - Jinyuan Wang, Aug 02 2019

			a(8) = 62 because 62^3 = 238328, which contains exactly three distinct digits.

Cf. A000533, A202940, A030294, A052051.

[k:k in [1..10000001]| k mod 10 ne 0 and  #Set(Intseq(k^3)) eq 3]; // Marius A. Burtea, Aug 02 2019

Select[Range[10001], Mod[#, 10] > 0 && Length@ Union@ IntegerDigits[#^3] == 3 &] (* Giovanni Resta, Sep 05 2019 *)

is(k) = #vecsort(digits(k^3), , 8)==3 && k%10!=0; \\ Jinyuan Wang, Aug 02 2019

More terms from Jinyuan Wang, Aug 02 2019

a(23)-a(25) from Jon E. Schoenfield, Aug 02 2019

cp's OEIS Frontend

User: Andrej Jakobcic

A383430 a(n) is the size of the largest subset of {1,...,n} such that no two elements differ by 5 or 8.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

Formula

A380770 Number of letters in the Slovene name of n (feminine, nominative), excluding spaces.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

A380433 Numbers that are a sum of both four and six consecutive prime numbers.

Views

Author

Keywords

Comments

Examples

Crossrefs

A308708 Numbers k such that k^3 contains exactly three distinct digits; numbers with trailing zeros are excluded.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions