A167619 Numbers k which have nonzero digital product equal to the last digits of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 111, 112, 113, 114, 115, 116, 117, 118, 119, 236, 315, 324, 612, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1236, 1315, 1324, 1612, 2136, 2312, 3115, 3124, 3212, 4384, 5175, 6112, 7735

Offset

1,2

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Formula

a(n) < 10^n, since 11...1 is always a member of this sequence; for n > 18, a(n) > n^1.0479 because 0's are not allowed in the decimal expansion.

Example

4384 is a term because 4*3*8*4 = 384 and the last digits of 4384 are 384.

Prog

(PARI) dprod(n)=my(pr=1); while(n, pr*=n%10; n\=10); pr
isA167619(n)=my(d=dprod(n)); d>0&&d==n%10^(#Str(d))
(Python)
A167619 = []
for k in range(1, 7736):
    dprod, k_str = 1, str(k)
    for d in range(0, len(k_str)): dprod *= int(k_str[d])
    if dprod != 0 and str(dprod) == k_str[-(len(str(dprod))):]: A167619.append(k)
print(A167619) # Karl-Heinz Hofmann, Jan 26 2024

Crossrefs

Sequence in context: A274125 A070698 A243079 * A020664 A055570 A083114

Adjacent sequences: A167616 A167617 A167618 * A167620 A167621 A167622

Keyword

nonn,base

Author

Claudio Meller, Nov 07 2009

Extensions

Formula and programs by Charles R Greathouse IV, Nov 09 2009

Status

approved