A053837 -id:A053837 - cp's OEIS frontend

A128244 Let s be the sum of the digits of n; a(n) is the product of the digits of s.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, May 03 2007

The sequence is equal to A053837 up to the 488th term.

			a(345)=2 because 3+4+5=12 and 1*2=2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A053837, A007953, A007954.

P:=proc(n) local i,k,w; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; k:=w; w:=1; while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; print(w); od; end: P(500);
# alternative
f:= n -> convert(convert(convert(convert(n,base,10),`+`),base,10),`*`):
map(f, [$1..100]); # Robert Israel, Dec 09 2016

sdpd[n_]:=Module[{s=Total[IntegerDigits[n]]},Times@@IntegerDigits[s]]; Array[sdpd, 110] (* Harvey P. Dale, Dec 17 2013 *)

a(n) = A007954(A007953(n)). - Michel Marcus, Dec 09 2016

Offset corrected by Robert Israel, Dec 09 2016

A171772 Number of steps needed to reach a prime when the map S(n)+M(n) is applied to n, or -1 if a prime is never reached. Here S(n) and M(N) mean the sum and the product of the digits of n in base 10.

Original entry on oeis.org

1, 0, 0, 3, 0, 2, 0, 2, 2, 2, 0, 1, 0, 3, 1, 1, 0, 1, 0, 1, 1, 3, 0, 4, 1, 2, 1, 3, 0, 1, 0, 1, 2, 1, 1, 2, 0, 2, -1, 4, 0, 4, 0, 5, 1, 2, 0, 6, -1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 3, 0, 2, 2, 2, 1, 7, 0, 3, -1, 1, 0, 1, 0, -1, 1, 3, 3, 1, 0, 3

Offset: 1

R. J. Mathar, Oct 12 2010

a(n)=0 if n is a prime.

			a(4)=3 because 4->8->16->13 is prime.
a(39)=-1 because 39 -> 39 ->39 ... never reaches a prime.
a(49)=-1 because 49 -> 49 ->49 ... never reaches a prime.
a(69)=-1 because 69 -> 69 ->69 ... never reaches a prime.
a(74)=-1 because 74 -> 39 ->39 ... never reaches a prime.
a(28)=3 because 28 ->26 ->20 ->2.

Robert Israel, Table of n, a(n) for n = 1..10000

A variant of A074871.

Cf. A007954, A053837, A061762.

f:= proc(n) local L;
  L:= convert(n,base,10);
  convert(L,`+`)+convert(L,`*`);
end proc:
g:= proc(n) option remember; local v,w;
     if n::prime then return 0 fi;
     v:= f(n);
     if v = n then return -1 fi;
     w:= procname(v);
     if w = -1 then -1 else w+1 fi
end proc:
map(g, [$1..100]); # Robert Israel, Nov 03 2019

A380192 Sum mod(10) of digits of n-th prime.

Original entry on oeis.org

2, 3, 5, 7, 2, 4, 8, 0, 5, 1, 4, 0, 5, 7, 1, 8, 4, 7, 3, 8, 0, 6, 1, 7, 6, 2, 4, 8, 0, 5, 0, 5, 1, 3, 4, 7, 3, 0, 4, 1, 7, 0, 1, 3, 7, 9, 4, 7, 1, 3, 8, 4, 7, 8, 4, 1, 7, 0, 6, 1, 3, 4, 0, 5, 7, 1, 7, 3, 4, 6, 1, 7, 6, 3, 9, 4, 0, 9, 5, 3, 4, 7, 8, 0, 6, 1, 7, 6, 1, 3, 7, 0, 9

Offset: 1

Enrique Navarrete, Jan 15 2025

All remainders 0,...,9 occur in this sequence.

Paolo Xausa, Table of n, a(n) for n = 1..10000
Enrique Navarrete, Distributions of Sums of Digits of Primes

Cf. A007605, A010879, A053837, A158293.

Mod[DigitSum[Prime[Range[100]]], 10] (* Paolo Xausa, Feb 06 2025 *)

a(n) = sumdigits(prime(n)) % 10; \\ Michel Marcus, Jan 16 2025

a(n) = A010879(A007605(n)).

A226468 Numbers in which each digit equals the sum (mod 10) of the other digits.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 505, 550, 5005, 5050, 5500, 5555, 50005, 50050, 50500, 50555, 55000, 55055, 55505, 55550, 500005, 500050, 500500, 500555, 505000, 505055, 505505, 505550, 550000, 550055, 550505, 550550, 555005, 555050, 555500, 555555, 1111116

Offset: 1

Michel Lagneau, Jun 08 2013

The primitive terms in this sequence are 11, 22, 33, 44, 55, 66, 77, 88, 99, 505, 5005, 5555, 50005, 50555, 500005, 500555, 555555, 1111116, 1111666, 1166666, 2222222, 2222277, ...; the other terms are built from the permutations of the digits of these numbers.
We find the following subsequences:
505, 5005, 50005, 500005, ..., 5000000005;
55, 5555, 555555, 55555555, ..., 5555555555.

			505 is in the sequence because the digits 5,0,5 satisfy
  5 = (0 + 5) mod 10;
  0 = (5 + 5) mod 10;
  5 = (5 + 0) mod 10.

Cf. A007953, A053837.

Select[Range[10^5], IntegerDigits[#] == Mod[Total[IntegerDigits[#]] - IntegerDigits[#], 10] &]

Edited by Jon E. Schoenfield, Sep 09 2017

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A128244 Let s be the sum of the digits of n; a(n) is the product of the digits of s.

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A171772 Number of steps needed to reach a prime when the map S(n)+M(n) is applied to n, or -1 if a prime is never reached. Here S(n) and M(N) mean the sum and the product of the digits of n in base 10.

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A380192 Sum mod(10) of digits of n-th prime.

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A226468 Numbers in which each digit equals the sum (mod 10) of the other digits.

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Mathematica

Extensions