A358012 Minimal number of coins needed to pay n cents using coins of denominations 1 and 5 cents.

0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12, 9, 10, 11, 12, 13, 10, 11, 12, 13, 14, 11, 12, 13, 14, 15, 12, 13, 14, 15, 16, 13, 14, 15, 16, 17, 14, 15, 16, 17, 18, 15, 16

Offset: 0

Author

Sandra Snan, Oct 24 2022

Keywords

• nonn
• easy

Comments

Sequence consists of runs of five consecutive integers: 0..4, 1..5, 2..6, 3..7, etc.

Links

• Index entries for sequences related to making change.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A002266, A010874.

Cf. A076314 (1,10 cents), A053344 (1,5,10,25 cents).

Programs

Mathematica

Array[Total@ QuotientRemainder[#, 5] &, 77, 0] (* Michael De Vlieger, Nov 03 2022 *)

PARI

a(n) = n\5 + n%5 \\ Thomas Scheuerle, Oct 24 2022

PARI

a(n) = vecsum(divrem(n, 5)); \\ Michel Marcus, Nov 03 2022

Python

def a(n): return n//5 + n%5 # Michael S. Branicky, Nov 03 2022

Formula

Sum of quotient and remainder of n/5.

a(n) = A002266(n) + A010874(n).