

A257850


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


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
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OFFSET

0,13


COMMENTS

Equivalently, write n in base 10, multiply the last digit by the number with its last digit removed.
See A142150(n1) 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).


FORMULA

a(n) = 2*a(n10)a(n20).  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) / ((x1)^2*(x+1)^2*(x^4x^3+x^2x+1)^2*(x^4+x^3+x^2+x+1)^2).  Colin Barker, May 11 2015


MATHEMATICA

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


PROG

(PARI) a(n, b=10)=(n=divrem(n, b))[1]*n[2]
(MAGMA) [Floor(n/10)*(n mod 10): n in [0..100]]; // Vincenzo Librandi, May 11 2015
(PARI) concat([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], Vec(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) / ((x1)^2*(x+1)^2*(x^4x^3+x^2x+1)^2*(x^4+x^3+x^2+x+1)^2) + O(x^100))) \\ Colin Barker, May 11 2015


CROSSREFS

Cf. A142150 (the base 2 analog), A115273, A257844  A257849.
Cf. also A007954, A035930, A171765, A257297.
Sequence in context: A088118 A088117 A330633 * A080464 A171765 A257297
Adjacent sequences: A257847 A257848 A257849 * A257851 A257852 A257853


KEYWORD

nonn,base,easy


AUTHOR

M. F. Hasler, May 10 2015


STATUS

approved



