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A349194 a(n) is the product of the sum of the first i digits of n, as i goes from 1 to the total number of digits of n. 9
1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 49, 56, 63, 70, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The only primes in the sequence are 2, 3, 5 and 7. - Bernard Schott, Nov 23 2021

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Malo David, About the Product Sum Digit Sequence

FORMULA

For n>10: a(n) = a(A059995(n))*A007953(n) where A059995(n) = floor(n/10).

In particular, for n<100: a(n) = floor(n/10)*A007953(n)

From Bernard Schott, Nov 23 2021: (Start)

a(n) = 1 iff n = 10^k, k >= 0 (A011557).

a(n) = 2 iff n = 10^k + 1, k >= 0 (A000533 \ {1}).

a(n) = 3 iff n = 10^k + 2, k >= 0 (A133384).

a(n) = 5 iff n = 10^k + 4, k >= 0.

a(n) = 7 iff n = 10^k + 6, k >= 0. (End)

From Marius A. Burtea, Nov 23 2021: (Start)

a(A002275(n)) = n! = A000142(n), n >= 1.

a(A090843(n - 1)) = (2*n - 1)!! = A001147(n), n >= 1.

a(A097166(n)) = (3*n - 2)!!! = A007559(n).

a(A093136(n)) = 2^n = A000079(n).

a(A093138(n)) = 3^n = A000244(n). (End)

EXAMPLE

For n=256, a(256) = 2*(2+5)*(2+5+6) = 182.

MATHEMATICA

Table[Product[Sum[Part[IntegerDigits[n], j], {j, i}], {i, Length[IntegerDigits[n]]}], {n, 74}] (* Stefano Spezia, Nov 10 2021 *)

PROG

(PARI) a(n) = my(d=digits(n)); prod(i=1, #d, sum(j=1, i, d[j])); \\ Michel Marcus, Nov 10 2021

(PARI) first(n)=if(n<9, return([1..n])); my(v=vector(n)); for(i=1, 9, v[i]=i); for(i=10, n, v[i]=sumdigits(i)*v[i\10]); v \\ Charles R Greathouse IV, Dec 04 2021

(Python)

from math import prod

from itertools import accumulate

def a(n): return prod(accumulate(map(int, str(n))))

print([a(n) for n in range(1, 100)]) # Michael S. Branicky, Nov 10 2021

(MAGMA) f:=func<n|&*[&+[Reverse(Intseq(n))[i]:i in [1..j]]:j in [1..#Intseq(n)]]>; [f(n):n in [1..100]]; // Marius A. Burtea, Nov 23 2021

CROSSREFS

Cf. A055642, A284001 (binary analog), A349190 (fixed points).

Cf. A007953 (sum of digits), A059995 (floor(n/10)).

Cf. A349278 (similar, with the last digits).

Cf. A349898, A349899.

Sequence in context: A080463 A209685 A114570 * A342829 A247796 A326344

Adjacent sequences:  A349191 A349192 A349193 * A349195 A349196 A349197

KEYWORD

nonn,base,look

AUTHOR

Malo David, Nov 10 2021

STATUS

approved

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Last modified July 4 12:35 EDT 2022. Contains 355075 sequences. (Running on oeis4.)