A257850 a(n) = floor(n/10) * (n mod 10).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8

Offset: 0

Author

M. F. Hasler, May 10 2015

Keywords

• nonn
• base
• easy

Comments

Equivalently, write n in base 10, multiply the last digit by the number with its last digit removed.

See A142150(n-1) for the base 2 analog and A257843 - A257849 for the base 3 - base 9 variants.

The first 100 terms coincide with those of A035930 (maximal product of any two numbers whose concatenation is n), A171765 (product of digits of n, or 0 for n<10), A257297 ((initial digit of n)*(n with initial digit removed)), but the sequence is of course different from each of these three.

The terms a(10) - a(100) also coincide with those of A007954 (product of decimal digits of n).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A142150 (the base 2 analog), A115273, A257844 - A257849.

Cf. also A007954, A035930, A171765, A257297.

Programs

Magma

[Floor(n/10)*(n mod 10): n in [0..100]]; // Vincenzo Librandi, May 11 2015

Mathematica

Table[Floor[n/10] Mod[n, 10], {n, 100}] (* Vincenzo Librandi, May 11 2015 *)

PARI

a(n,b=10)=(n=divrem(n,b))[1]*n[2]

Python

def A257850(n): return n//10*(n%10) # M. F. Hasler, Sep 01 2021

Formula

a(n) = 2*a(n-10)-a(n-20). - Colin Barker, May 11 2015

G.f.: x^11*(9*x^8+8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)^2*(x+1)^2*(x^4-x^3+x^2-x+1)^2*(x^4+x^3+x^2+x+1)^2). - Colin Barker, May 11 2015