A111707 -id:A111707 - cp's OEIS frontend

A257297 a(n) = (initial digit of n) * (n with initial digit removed).

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, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 1, 2, 3

Offset: 0

M. F. Hasler, May 10 2015

The initial 100 terms match those of A035930 (maximal product of any two numbers whose concatenation is n) and also those of A171765 (product of digits of n, or 0 for n<10), and except for initial terms, also A007954 (product of decimal digits of n) and A115300 (greatest digit of n * least digit of n).
Iterations of this map always end in 0, since a(n) < n. Sequence A257299 lists numbers for which these iterations reach 0 in exactly 9 steps, with the additional constraint of having each time a different initial digit.
If "initial" is replaced by "last" in the definition (A257850), then we get the same values up to a(100), but (10, 20, 30, ...) for n = 101, 102, 103, ..., again different from each of the 4 other sequences mentioned in the first comment. - M. F. Hasler, Sep 01 2021

			For n<10, a(n) = n*0 = 0, since removing the initial and only digit leaves nothing, i.e., zero (by convention).
a(10) = 1*0 = 0, a(12) = 1*2 = 2, ..., a(20) = 2*0 = 0, a(21) = 2*1 = 2, a(22) = 2*2 = 4, ...
a(99) = 9*9 = 81, a(100) = 1*00 = 0, a(101) = 1*01 = 1, ..., a(123) = 1*23, ...

Cf. A257850, A007954, A035930, A080464, A115300, A169669, A111707, A088117, A187844.

a:= n-> `if`(n<10, 0, (s-> parse(s[1])*parse(s[2..-1]))(""||n)):
seq(a(n), n=0..120);  # Alois P. Heinz, Feb 12 2024

Table[Times@@FromDigits/@TakeDrop[IntegerDigits@n,1],{n,0,103}] (* Giorgos Kalogeropoulos, Sep 03 2021 *)

apply( {A257297(n)=vecprod(divrem(n,10^logint(n+!n,10)))}, [0..111]) \\ Edited by M. F. Hasler, Sep 01 2021

def a(n): s = str(n); return 0 if len(s) < 2 else int(s[0])*int(s[1:])
print([a(n) for n in range(104)]) # Michael S. Branicky, Sep 01 2021

For 1 <= m <= 9 and n < 10^k, a(m*10^k + n) = m*n.

a(101..103) corrected by M. F. Hasler, Sep 01 2021

A115300 Greatest digit of n * least digit of n.

Original entry on oeis.org

1, 4, 9, 16, 25, 36, 49, 64, 81, 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: 1

Rick L. Shepherd, Jan 20 2006

a(101) = 0 and A111707(101) = 1, but all previous terms match.

a(n) = A169669(n) for n <= 100.

			a(3) = 3 * 3 = 9, a(232) = 3 * 2 = 6, a(1889009898) = 9 * 0 = 0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A037904 (greatest-least), A115299 (greatest+least), A111707.

Cf. A054054, A054055, A169669.

a115300 n = a054054 n * a054055 n  -- Reinhard Zumkeller, Apr 29 2015

Array[Max[#] * Min[#] &@ IntegerDigits[#] &, 81] (* James C. McMahon, Aug 18 2024 *)

a(n) = my(d=digits(n)); vecmin(d)*vecmax(d); \\ Michel Marcus, Aug 18 2024

def a(n): d = list(map(int, str(n))); return max(d) * min(d)
print([a(n) for n in range(1, 82)]) # Michael S. Branicky, Dec 12 2023

a(n) = A054054(n)*A054055(n). - Reinhard Zumkeller, Apr 29 2015

A169669 (first digit of n) * (last digit of n) in decimal representation.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 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

Offset: 0

Reinhard Zumkeller, Apr 05 2010

a(n) = A000030(n)*A010879(n);
a(n) = A115300(n) for n<=100, A115300(101) = 0;
a(n) = A111707(n) for n<=109, A111707(110) = 1;
0 <= a(n) <= 81, range = A174995;
a(10*n + n mod 10) = a(n);
a(A008592(n)) = 0;
A000030(a(A017281(n))) = A000030(A017281(n));
a(n) = a(A004086(n))*A168184(n);

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A088133.

Cf. A000030, A008592, A010879, A111707, A115300, A174995.

a169669 n = a000030 n * mod n 10
-- Reinhard Zumkeller, Apr 29 2015

def a(n): return int(str(n)[0])*(n%10)
print([a(n) for n in range(81)]) # Michael S. Branicky, Jul 13 2022

A085942 Write digit reversal of n below n. Then a(n) = the sum of the product of digits in the same column.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 0, 14, 28, 42, 56, 70, 84

Offset: 0

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 14 2003

a(n) = sum of the products of r-th most significant digit and the r-th least significant digit, the sum being taken over all the digits of n.
If the number of digits in n is even then a(n) is also even.
a(36) = 36.

			a(4) = 4*4 = 16.
a(123) = 10: 123
............ 321 (1*3 +2*2 +3*1 = 10).
a(1203) = 1*3 + 2*0 + 0*2 +3*1 = 6.
a(1234) = 1*4 +2*3 + 3*2 +4*1 = 20.

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Cf. A111707.

dr[n_]:=Module[{idn=IntegerDigits[n]},Total[Times@@@Transpose[Join[{idn, Reverse[idn]}]]]]; Array[dr,80] (* Harvey P. Dale, May 03 2011 *)

a(n) = { my (d=digits(n)); d*Colrev(d) } \\ Rémy Sigrist, May 21 2021

More terms from David Wasserman, Feb 14 2005
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 31 2007
a(0) = 0 prepended by Rémy Sigrist, May 21 2021

cp's OEIS Frontend

A257297 a(n) = (initial digit of n) * (n with initial digit removed).

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A115300 Greatest digit of n * least digit of n.

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A169669 (first digit of n) * (last digit of n) in decimal representation.

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A085942 Write digit reversal of n below n. Then a(n) = the sum of the product of digits in the same column.

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