A217404 -id:A217404 - cp's OEIS frontend

A217419 Numbers factoring 3^r*11^s whose decimal representations are such that each of the digits 0-9 appears a prime number of times.

5586701408957811048315412506328906443, 4756351651546448722293215379849833244291829764770574840668685771747

Offset: 1

James G. Merickel, Oct 05 2012

The 3-adic valuations for the terms are 29 and 83, and the 11-adic valuations are 22 and 26. For the other main sequences of trios corresponding to nonsquare semiprimes other than 10 and through 39, including separate prime valuations in companion sequences, see cross-references.
While heuristics imply this sequence is infinite, finding a(3) is difficult: A program counting digits for numbers of the given form restricted to those having an even number of decimal digits (with heuristics and initial data practically ruling out counts of 2 for any digit) produced no result for this sequence through 61 values having no more than one digit counted a nonprime number of times. The last of these values was 3^14650*11^3032 (10148 digits in length). - James G. Merickel, Dec 11 2013
a(3) if it exists has > 10000 digits. - James G. Merickel, Dec 11 2013

			3^29 * 11^22 has two each of 2's, 7's and 9's; three each of 3's and 6's; and five each of 0's, 1's, 4's, 5's and 8's.  No smaller number with only 3 and 11 as prime factors has a prime number of each digit 0-9, so a(1) is this value.

Cf. A217854, A217404, A217407, A217410, A217413, A217416, A217422, A217425, A217428, A217431.

{
k=33;a=[99];t=1;while(1,
v=vectorsmall(10);m=k;
while(m,d=m%10;m\=10;v[d+1];next());
f=1;for(i=1,10,if(isprime(v[i])==0,f=0;break()));
if(f,F=factor(k);print1(3"^"F[1,2]"*"11"^"F[2,2]"="k"\n"));
if(11^(t+1)

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

A217419 Numbers factoring 3^r*11^s whose decimal representations are such that each of the digits 0-9 appears a prime number of times.

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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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cp's OEIS Frontend

A217419 Numbers factoring 3^r*11^s whose decimal representations are such that each of the digits 0-9 appears a prime number of times.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

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.

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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.