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A174138
Numbers congruent to {5,6,7,8,9,15,16,17,18,19} mod 25.
3
5, 6, 7, 8, 9, 15, 16, 17, 18, 19, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 55, 56, 57, 58, 59, 65, 66, 67, 68, 69, 80, 81, 82, 83, 84, 90, 91, 92, 93, 94, 105, 106, 107, 108, 109, 115, 116, 117, 118, 119, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 155, 156, 157
OFFSET
1,1
COMMENTS
Numbers whose partition into parts of sizes 1, 5, 10, and 25 having a minimal number of parts includes a part of size 5.
For each number the partition is unique and exactly one part is of size 5.
Complement of A174139.
Amounts in cents requiring a nickel when the minimal number of coins is selected from pennies, nickels, dimes, and quarters (whether usage of bills for whole-dollar amounts is permitted or not).
For each n >= 0, floor(n/25) parts of size 25 (quarters) occur in the partition with minimal number of these parts (regardless of whether partition includes part of size 5).
FORMULA
a(10+n) = a(n) + 25 for n >= 1.
a(n) = a(n-1) + a(n-10) - a(n-11). G.f.: x*(5+x+x^2+x^3+x^4+6*x^5+x^6+x^7+x^8+x^9+6*x^10) / ( (1+x) *(x^4+x^3+x^2+x+1) *(x^4-x^3+x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
a(n) = n+9+5*floor((floor((n-1)/5)-1)/2)+10*floor(floor((n-1)/5)/2). - Wesley Ivan Hurt, Mar 22 2015
EXAMPLE
As 15 = 10 + 5, 15 is a term since 5 is included and all other candidate partitions have more than two parts. Similarly, as 30 = 25 + 5, 30 is a term. However, 45 = 25 + 10 + 10 is not a term as it contains no part of size 5.
MATHEMATICA
Table[n + 9 + 5 Floor[(Floor[(n - 1)/5] - 1)/2] + 10 Floor[Floor[(n - 1)/5]/2], {n, 100}] (* Wesley Ivan Hurt, Mar 22 2015 *)
PROG
(Magma) [n : n in [1..200] | n mod 25 in [5, 6, 7, 8, 9, 15, 16, 17, 18, 19]]; // Vincenzo Librandi, Mar 22 2015
CROSSREFS
Cf. A174139, A174140, A174141, A047201 (requires at least one part of size 1 (penny)), A008587, A053344 (minimal number of parts), A001299 (number of all such partitions).
Sequence in context: A285219 A047577 A293481 * A108401 A125298 A037362
KEYWORD
easy,nonn
AUTHOR
Rick L. Shepherd, Mar 09 2010
STATUS
approved