A349864 -id:A349864 - cp's OEIS frontend

A349278 a(n) is the product of the sum of the last i digits of n, with i going from 1 to the total number of digits of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 0, 3, 8, 15, 24, 35, 48, 63, 80, 99, 0, 4, 10, 18, 28, 40, 54, 70, 88, 108, 0, 5, 12, 21, 32, 45, 60, 77, 96, 117, 0, 6, 14, 24, 36, 50, 66, 84, 104, 126, 0, 7, 16, 27, 40, 55, 72, 91, 112, 135, 0

Offset: 1

Michel Marcus, Nov 13 2021

This is similar to A349194 but with digits taken in reversed order.
The only primes in the sequence are 2, 3, 5 and 7. - Bernard Schott, Dec 04 2021
The positive terms form a subsequence of A349194. - Bernard Schott, Dec 19 2021

			For n=256, a(256) = 6*(6+5)*(6+5+2) = 858.

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A349194, A349279 (fixed points).

Cf. A349864, A349865.

a[n_] := Times @@ Accumulate @ Reverse @ IntegerDigits[n]; Array[a, 70] (* Amiram Eldar, Nov 13 2021 *)

a(n) = my(d=Vecrev(digits(n))); prod(i=1, #d, sum(j=1, i, d[j]));

from math import prod
from itertools import accumulate
def a(n): return 0 if n%10==0 else prod(accumulate(map(int, str(n)[::-1])))
print([a(n) for n in range(1, 71)]) # Michael S. Branicky, Nov 13 2021

From Bernard Schott, Dec 04 2021: (Start)
a(n) = 0 iff n is a multiple of 10 (A008592).
a(n) = 1 iff n = 1.
a(n) = 2 (resp. 3, 4, 5, 7, 9) iff n = 10^k+1 (A000533) (resp. 2*10^k+1 (A199682), 3*10^k+1 (A199683), 4*10^k+1 (A199684), 6*10^k+1 (A199686), 8*10^k+1 (A199689)).
a(R_n) = n! where R_n = A002275(n) is repunit > 0, and n! = A000142(n).
a(n) = A349194(n) if n is palindrome (A002113). (End)

A349865 Composite numbers that are missing from A349278.

Original entry on oeis.org

25, 26, 34, 38, 39, 46, 49, 51, 57, 58, 62, 68, 69, 74, 75, 76, 82, 85, 86, 87, 92, 93, 94, 95, 102, 106, 111, 114, 115, 116, 118, 119, 121, 122, 123, 124, 125, 129, 133, 134, 138, 141, 142, 143, 145, 146, 147, 148, 152, 155, 158, 159, 161, 164, 166, 169, 171, 172, 174, 177, 178

Offset: 1

Bernard Schott, Dec 03 2021

Since no prime >= 11 is a term in A349278, only composite numbers are listed here.

			There does not exist an integer d.u, where . stands for concatenation, such that 26 = u*(u+d), so 26 is a term.
As 28 = A349278(34) = 4*(4+3), 28 is not a term.

Cf. A349278, A349864.

Equals disjoint union of A349733 and A350061.

More terms from Michel Marcus, Dec 04 2021

cp's OEIS Frontend

A349278 a(n) is the product of the sum of the last i digits of n, with i going from 1 to the total number of digits of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula