cp's OEIS Frontend

A342112 Drop the final digit of n^5.

%I A342112 #14 Mar 07 2021 18:58:51
%S A342112 0,0,3,24,102,312,777,1680,3276,5904,10000,16105,24883,37129,53782,
%T A342112 75937,104857,141985,188956,247609,320000,408410,515363,643634,796262,
%U A342112 976562,1188137,1434890,1721036,2051114,2430000,2862915,3355443,3913539,4543542,5252187,6046617
%N A342112 Drop the final digit of n^5.
%C A342112 Why exponent 5? Because it is the smallest nontrivial exponent e such that for an integer k not ending in 0, 1, 5 and 6, k^e has the same unit digit of k in base 10.
%H A342112 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10, 10,-5,1,0,0,0,0,1,-5,10,-10,5,-1).
%H A342112 <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>.
%F A342112 G.f.: x^2*(3 + 9*x + 12*x^2 + 12*x^3 + 12*x^4 + 12*x^5 + 12*x^6 + 12*x^7 + 13*x^8 + 8*x^9 + 15*x^10 - x^11 + x^12)/((1 - x)^6*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9)).
%F A342112 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + a(n-10) - 5*a(n-11) + 10*a(n-12) - 10*a(n-13) + 5*a(n-14) - a(n-15) for n > 14.
%F A342112 a(n) = floor(n^5/10).
%F A342112 a(n) = (A000584(n) - A010879(n))/10.
%F A342112 a(n) = A164938(n) + A059995(n).
%t A342112 Table[(n^5-Last[IntegerDigits[n]])/10,{n,0,36}]
%Y A342112 Cf. A000584, A010879, A016813, A056865, A059995, A061167, A164938.
%K A342112 nonn,base,easy
%O A342112 0,3
%A A342112 _Stefano Spezia_, Feb 28 2021