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Numbers > 24 that are congruent to {5,6,7,8,9} mod 10.
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%I #22 Nov 26 2024 15:30:05

%S 25,26,27,28,29,35,36,37,38,39,45,46,47,48,49,55,56,57,58,59,65,66,67,

%T 68,69,75,76,77,78,79,85,86,87,88,89,95,96,97,98,99,105,106,107,108,

%U 109,115,116,117,118,119,125,126,127,128,129,135,136,137,138,139,145,146

%N Numbers > 24 that are congruent to {5,6,7,8,9} mod 10.

%C Amounts in cents of coins in denominations 1, 5 and 10 cents that must include change for a 25-cent coin. Regarding currently-minted US coins, note that the 25-cent quarter is the only denomination for which a smaller denomination exists (the 10-cent dime) which is not a divisor. As a result, an amount that may consist only of any number of dimes and up to four 1-cent pennies does not guarantee change for a quarter.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F a(n) = 10 + a(n-5) for n >= 6.

%F From _Chai Wah Wu_, Jun 10 2016: (Start)

%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

%F G.f.: x*(-19*x^5 + x^4 + x^3 + x^2 + x + 25)/(x^6 - x^5 - x + 1). (End)

%F a(n) = 25 + ((n-1) mod 5) + 10*floor((n-1)/5). - _Wesley Ivan Hurt_, Nov 03 2016

%t Table[25 + Mod[n - 1, 5] + 10*Floor[(n - 1)/5], {n, 50}] (* _Wesley Ivan Hurt_, Nov 03 2016 *)

%t LinearRecurrence[{1,0,0,0,1,-1},{25,26,27,28,29,35},70] (* _Harvey P. Dale_, Nov 26 2024 *)

%o (PARI) is(n) = n > 24 && n % 10 > 4 \\ _Felix Fröhlich_, Nov 03 2016

%o (Magma) [n : n in [25..150] | n mod 10 in [5..9]]; // _Vincenzo Librandi_, Nov 04 2016

%Y Cf. A130734.

%K easy,nonn

%O 1,1

%A _Rick L. Shepherd_, May 05 2008