A063543 -id:A063543 - cp's OEIS frontend

A063114 a(n) = n + product of the nonzero digits of n.

2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 22, 23, 26, 29, 32, 35, 38, 41, 44, 47, 33, 34, 38, 42, 46, 50, 54, 58, 62, 66, 44, 45, 50, 55, 60, 65, 70, 75, 80, 85, 55, 56, 62, 68, 74, 80, 86, 92, 98, 104, 66, 67, 74, 81, 88, 95, 102, 109, 116

Offset: 1

N. J. A. Sloane, Aug 08 2001

			a(59) = 59 + 5*9 = 104. a(66) = 66 + 6*6 = 102.

Harry J. Smith, Table of n, a(n) for n = 1..1000
P. A. Loomis, An Interesting Family of Iterated Sequences
P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151.
P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151. [Annotated archived copy]
Index entries for Colombian or self numbers and related sequences

Cf. A051801, A063108, A063112, A063113, A063543.

var stk: stack; end; for n := 1 to 80 do s := itoa(n); for j := 0 to length(s) -1 do k := atoi(s[j..j]); if k > 0 then stack_push(stk,k); end; end; write(n + product(stack2array(stk))," "); end;

a063114 n = n + a051801 n -- Reinhard Zumkeller, Jan 15 2012

Table[i+Times@@(IntegerDigits[i]/. 0->1), {i, 70}]

a(n) = n + vecprod(select(x->(x!=0), digits(n))) \\ Harry J. Smith, Aug 19 2009

a(n) = n + A051801(n). - Reinhard Zumkeller, Jan 15 2012

More terms from Robert G. Wilson v and Klaus Brockhaus, Aug 09 2001

A062329 a(n) = (sum of digits of n) - (product of digits of n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, 3, 1, -1, -3, -5, -7, -9, -11, -13, -15, 4, 1, -2, -5, -8, -11, -14, -17, -20, -23, 5, 1, -3, -7, -11, -15, -19, -23, -27, -31, 6, 1, -4, -9, -14, -19, -24, -29, -34, -39, 7, 1, -5, -11, -17, -23, -29, -35, -41, -47, 8, 1, -6, -13, -20, -27

Offset: 0

Amarnath Murthy, Jun 21 2001

			a(23) = 2 + 3 - 2*3 = -1.
a(49) = -(4*9) + (4 + 9) = -36 + 13 = -23.

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A007953, A007954, A034710, A062996, A062997, A062998, A062999, A070565.

A063543 has a similar graph.

a[n_] := (t = IntegerDigits[n]; Plus @@ t - Times @@ t); Table[ a[n], {n, 0, 75}] (* Robert G. Wilson v *)

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 22 2001

Signed version from Henry Bottomley, Jun 29 2001

A233783 The smallest prime that produces a set of n primes such that every prime after the first one is equal to the previous minus the product of its nonzero digits.

Original entry on oeis.org

2, 23, 251, 347, 5023, 50227, 64037, 3924211, 4952767, 43275737, 586635689, 592856489, 62527264517

Offset: 1

Carlos Rivera, Dec 15 2013

a(14) > 6.8*10^11. - Giovanni Resta, Dec 16 2013

			Example: for n = 3, initial prime is 251, because 251 -> 251 - 2*5*1 = 241 -> 241 - 2*4*1 -> 233.

Cf. A063543, A233692.

a(11)-a(13) from Giovanni Resta, Dec 16 2013

A246622 Primes of the form n + product of nonzero digits of n, in order of their occurrence.

Original entry on oeis.org

2, 11, 23, 29, 41, 47, 67, 109, 89, 107, 101, 167, 181, 223, 199, 227, 251, 293, 283, 349, 331, 433, 347, 461, 313, 383, 353, 379, 431, 457, 379, 443, 521, 547, 457, 491, 593, 499, 557, 673, 601, 823, 619, 653, 839, 607, 617, 631, 659, 673, 659, 743, 929, 919

Offset: 1

K. D. Bajpai, Aug 31 2014

Primes in A063114.

			a(2) = 11 which is prime. Also, 11 = 10 + 1, which is n + product of nonzero digit of n.
a(9) = 89 which is prime. Also, 89 = 81 + (8*1), which is n + product of nonzero digits of n.
a(10) = 107 which is prime. Also, 107 = 83 + (8*3), which is n + product of nonzero digits of n.

K. D. Bajpai, Table of n, a(n) for n = 1..13250

Cf. A000040, A063114, A063543.

Select[Table[n + Times @@ DeleteCases[IntegerDigits[n], 0], {n, 1000}], PrimeQ]

A329725 a(1)=0, a(n) = n - (product of nonzero digits of n) - a(n-1).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 17, 2, 16, 1, 15, 0, 14, -1, 13, -2, 29, -1, 27, -3, 25, -5, 23, -7, 21, -9, 45, -8, 42, -11, 39, -14, 36, -17, 33, -20, 65, -19, 61, -23, 57, -27, 53, -31, 49, -35, 89, -34, 84, -39, 79, -44, 74, -49, 69, -54, 117

Offset: 1

Joshua Oliver, Nov 19 2019

a(10n+1)-a(10n-1)=1 for all positive integer n (conjectured).

			a(22) = 22 - 2*2 - 2 = 16.

Joshua Oliver, Table of n, a(n) for n = 1..5000

Cf. A063108, A063543.

R:= ListTools:-PartialSums(map(n -> (-1)^n*(n - convert(subs(0=NULL,convert(n,base,10)),`*`)), [$1..100])):
seq((-1)^n*R[n],n=1..100); # Robert Israel, Nov 20 2019

Nest[Append[#1, #2 - Last[#1] - Times @@ DeleteCases[IntegerDigits[#2], 0]] & @@ {#, Length@ # + 1} &, {0}, 69] (* Michael De Vlieger, Nov 19 2019 *)

for (n=1, 70, print1 (v=if (n==1, 0, n - vecprod(select(sign, digits(n))) - v)", ")) \\ Rémy Sigrist, Nov 28 2019

a(n) = Sum_{k=2..n} (-1)^(n-k)*A063543(k). - Robert Israel, Nov 20 2019

cp's OEIS Frontend

A063114 a(n) = n + product of the nonzero digits of n.

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A062329 a(n) = (sum of digits of n) - (product of digits of n).

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A233783 The smallest prime that produces a set of n primes such that every prime after the first one is equal to the previous minus the product of its nonzero digits.

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Extensions

A246622 Primes of the form n + product of nonzero digits of n, in order of their occurrence.

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A329725 a(1)=0, a(n) = n - (product of nonzero digits of n) - a(n-1).

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