A217433 -id:A217433 - cp's OEIS frontend

A217431 Numbers of the form 3^r*13^s whose decimal representation has a prime number of copies of each digit 0-9.

691159348276025798403, 510798409623548623605717, 5097400863986495932124683149477, 10996481542736751381410324522244489, 915432679064411834115450778445909529

Offset: 1

James G. Merickel, Oct 05 2012

See the formula section for more data, and others in cross-reference for motivation and similar.

a(6), if it exists, is larger than 10^1000. - Giovanni Resta, Jan 16 2014

			a(1) = 3^25 * 13^8 (so A217432(1)=25 and A217432(1)=8). Indeed, it contains two copies of each digit other than 9 and three copies of 9.  No smaller 21-digit number with this general character -- two copies of all but one digit -- and no 20-digit number with two copies of each digit has form 3^a*13^b with a,b > 0.

Cf. A217854, A217432, A217433, A217404, A217407, A217410, A217413, A217416, A217419, A217422, A217425, A217428.

nd = 50; mx = 10^nd; pr = Prime@ Range@ PrimePi@ nd; pQ[n_] := Union[DigitCount@n, pr] == pr; Sort@ Select[ Flatten@ Table[3^p*13^q, {p, Log[3, mx/13]}, {q, Log[13, mx/3^p]}], pQ] (* terms < 10^50, Giovanni Resta, Jan 16 2014 *)

A217431(n) = 3^A217432(n) * 13^A217433(n).

A217432 3-adic valuation of A217431.

Original entry on oeis.org

25, 10, 20, 48, 10

Offset: 1

James G. Merickel, Oct 03 2012

A217431 consists of numbers of the form (3^r)*(13^s). This sequence holds the r values.

Cf. A217431, A217433.

A218005 Nonsquare semiprimes pq (10 excluded) giving record large smallest number p^r q^s such that each decimal digit appears a prime number of times.

Original entry on oeis.org

6, 14, 15, 33, 57, 185, 237, 247, 291, 327, 403

Offset: 1

James G. Merickel, Oct 17 2012

The idea for this sequence derives from A216854 and A217404 through A217433. 10 is excluded as a special case, as it necessitates finding the smaller of powers of 2 and 5 to have no digit other than 0 not appearing a prime number of times (to then be multiplied by the first power of 10 to give prime count for this digit). Even the sparser sets of mere prime powers should have members satisfying the criterion; but the numbers can be quite large, and at time of submission the actual record value for this sequence's a(11) (13*31) is unknown. The record values to that point are: (2^56)*(3^12), (2^36)*(7^15), (3^35)*(5^17), (3^29)*(11^22), (3^24)*(19^22), (5^30)*(37^12), (3^48)*(79^9), (13^40)*(19^4), (3^16)*(97^26), and (3^248)*(109^244).

Cf. A216854, A217404, A217407, A217410, A217413, A217416, A217419, A217422, A217425, A217428, A217431.

cp's OEIS Frontend

A217431 Numbers of the form 3^r*13^s whose decimal representation has a prime number of copies of each digit 0-9.

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Formula

A217432 3-adic valuation of A217431.

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Author

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Comments

Crossrefs

A218005 Nonsquare semiprimes pq (10 excluded) giving record large smallest number p^r q^s such that each decimal digit appears a prime number of times.

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Author

Keywords

Comments

Crossrefs

cp's OEIS Frontend

A217431 Numbers of the form 3^r*13^s whose decimal representation has a prime number of copies of each digit 0-9.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula

A217432 3-adic valuation of A217431.

Views

Author

Keywords

Comments

Crossrefs

A218005 Nonsquare semiprimes p*q (10 excluded) giving record large smallest number p^r * q^s such that each decimal digit appears a prime number of times.

Views

Author

Keywords

Comments

Crossrefs

A218005 Nonsquare semiprimes pq (10 excluded) giving record large smallest number p^r q^s such that each decimal digit appears a prime number of times.