A342112 Drop the final digit of n^5.

0, 0, 3, 24, 102, 312, 777, 1680, 3276, 5904, 10000, 16105, 24883, 37129, 53782, 75937, 104857, 141985, 188956, 247609, 320000, 408410, 515363, 643634, 796262, 976562, 1188137, 1434890, 1721036, 2051114, 2430000, 2862915, 3355443, 3913539, 4543542, 5252187, 6046617

Offset: 0

Author

Stefano Spezia, Feb 28 2021

Keywords

• nonn
• base
• easy

Comments

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.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10, 10,-5,1,0,0,0,0,1,-5,10,-10,5,-1).
• Index entries for sequences related to final digits of numbers.

Crossrefs

Cf. A000584, A010879, A016813, A056865, A059995, A061167, A164938.

Programs

Mathematica

Table[(n^5-Last[IntegerDigits[n]])/10,{n,0,36}]

Formula

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)).

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.

a(n) = floor(n^5/10).

a(n) = (A000584(n) - A010879(n))/10.

a(n) = A164938(n) + A059995(n).