A107698 -id:A107698 - cp's OEIS frontend

A107694 Primes with digital product = 8.

181, 241, 421, 811, 1181, 1811, 2141, 2221, 2411, 4211, 8111, 21221, 141121, 142111, 411211, 1111181, 1112141, 1121221, 1211141, 1211411, 1212121, 2111411, 2121121, 2211211, 2221111, 2411111, 4121111, 4211111, 11221211, 12111221, 12121121

Offset: 1

Zak Seidov and Robert G. Wilson v, May 20 2005

Cf. A004022, A107612, A107689, A107690, A107691, A107692, A107693, A107695, A107696, A107697, A107698.

[p: p in PrimesUpTo(3*10^7) | &*Intseq(p) eq 8]; // Vincenzo Librandi, Jul 27 2016

Union[ Flatten[ Table[ Select[ Sort[ FromDigits /@ Join[ Permutations[ Flatten[{8, Table[1, {n}]}]], Permutations[ Flatten[{2, 4, Table[1, {n - 1}]}]], Permutations[ Flatten[{2, 2, 2, Table[1, {n - 2}]}] ]]], PrimeQ[ # ] & ], {n, 0, 7}]]]
Select[Prime[Range[3 10^6]], Times@@IntegerDigits[#] == 8 &] (* Vincenzo Librandi, Jul 27 2016 *)

A107697 Primes with digital product = 12.

Original entry on oeis.org

43, 223, 431, 1223, 1621, 2161, 2213, 3221, 6121, 6211, 11261, 11621, 12161, 12611, 13411, 21611, 26111, 41113, 41131, 61121, 61211, 111143, 111341, 111431, 112213, 114113, 114311, 121123, 121321, 122131, 123121, 131221, 141131, 141311, 143111

Offset: 1

Zak Seidov and Robert G. Wilson v, May 20 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..86

Cf. A004022, A107612, A107689, A107690, A107691, A107692, A107693, A107694, A107695, A107696, A107698.

[p: p in PrimesUpTo(1000000) | &*Intseq(p) eq 12]; // Vincenzo Librandi, Jul 27 2016

Union[ Flatten[ Table[ Select[ Sort[ FromDigits /@ Join[ Permutations[ Flatten[{2, 6, Table[1, {n - 1}]}]], Permutations[ Flatten[{3, 4, Table[1, {n - 1}]}]], Permutations[ Flatten[{2, 2, 3, Table[1, {n - 2}]}] ]]], PrimeQ[ # ] & ], {n, 0, 5}]]]
Select[Prime[Range[75000]], Times@@IntegerDigits[#] == 12 &] (* Vincenzo Librandi, Jul 27 2016 *)

A198487 Smallest nonprime positive numbers whose digital product = n, or 0 if impossible.

Original entry on oeis.org

10, 1, 12, 1113, 4, 15, 6, 117, 8, 9, 25, 0, 26, 0, 27, 35, 28, 0, 36, 0, 45, 371, 0, 0, 38, 55, 0, 39, 74, 0, 56, 0, 48, 0, 0, 57, 49, 0, 0, 0, 58, 0, 76, 0, 0, 95, 0, 0, 68, 77, 255, 0, 0, 0, 69, 0, 78, 0, 0, 0, 256, 0, 0, 791, 88, 0, 0, 0, 0, 0, 275, 0, 98, 0, 0, 355

Offset: 0

Jaroslav Krizek, Oct 25 2011

Zeros appear for n which are a member of A068191.

If the requirement "positive" is dropped, a(0) becomes 0 instead.

			a(21)=371 because 371 is  the smallest nonprime positive number whose digital product is 21 (3*7*1 = 21).

Cf. A107698 (smallest primes with digital product n)

A198378 Smallest prime with multiplicative digital root value 0 <= n <= 9.

Original entry on oeis.org

59, 11, 2, 3, 41, 5, 23, 7, 29, 19

Offset: 0

Jaroslav Krizek, Oct 23 2011

Cf. A107698, A198487.

A341634 Smallest prime whose product of digits (A007954) is the n-th 7-smooth number = A002473(n), with a(0) = 101.

Original entry on oeis.org

101, 11, 2, 3, 41, 5, 23, 7, 181, 19, 251, 43, 127, 53, 281, 29, 541, 37, 83, 11551, 139, 47, 523, 1481, 157, 149, 12451, 67, 59, 283, 11177, 2551, 239, 1187, 1453, 79, 881, 257, 89, 1553, 2851, 199, 347, 563, 1483, 277, 14551, 1753, 269, 827, 853, 15551, 367

Offset: 0

Bernard Schott, Feb 16 2021

For n>=1, equals A107698 without the zeros.

101 is the smallest prime with the digit 0, so A007954(101) = 0 but as 0 is not a 7-smooth number, it is chosen a(0) = 101.

			83 is prime, A007954(83) = 8*3 = 24 that is the 18th 7-smooth number, and as no prime < 83 has a product of digits = 24, a(18) = 83.

David A. Corneth, Table of n, a(n) for n = 0..10000 (first 646 terms from Robert Israel)

Cf. A002473, A004954, A007954, A053666, A107698, A335331.

pod[n_] := Times @@ IntegerDigits[n]; seq[max_] := Module[{sm7 = Join[{0}, Select[Range[max], Max[FactorInteger[#][[;; , 1]]] <= 7 &]], m, s, n, c, i, ind}, m = Length[sm7]; s = Table[0, {m}]; n = 1; c = 0; While[c < m, n = NextPrime[n]; i = pod[n]; If[MemberQ[sm7, i], ind = Position[sm7, i][[1, 1]]]; If[s[[ind]] == 0, c++; s[[ind]] = n]]; s]; seq[150] (* Amiram Eldar, Feb 16 2021 *)

a(n) = A107698(A002473(n)) for n>=1. - Amiram Eldar, Feb 17 2021

More terms from Amiram Eldar, Feb 16 2021

cp's OEIS Frontend

A107694 Primes with digital product = 8.

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A107697 Primes with digital product = 12.

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A198487 Smallest nonprime positive numbers whose digital product = n, or 0 if impossible.

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A198378 Smallest prime with multiplicative digital root value 0 <= n <= 9.

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A341634 Smallest prime whose product of digits (A007954) is the n-th 7-smooth number = A002473(n), with a(0) = 101.

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