cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A225334 Look-and-repeat: similar to look-and-say except frequency is repeated (seed 3).

Original entry on oeis.org

3, 113, 221113, 222331113, 332223331113, 223332333331113, 222333112553331113, 332333221112225333331113, 223112333222331332115553331113, 222113221112333332223111223112221335333331113
Offset: 1

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Author

Jean-Christophe Hervé, May 12 2013

Keywords

Comments

Look-and-repeat sequence A225329 with seed 3.
Contains 1, 2, 3 and 5, but not 4.
All terms end with 3 (the seed) and, starting at the fourth, with 3331113, which makes the 5 appear.
All terms except the second begin with 2 or 3; it is a direct consequence of the look-and-repeat rule.
Sequence A225333, the look-and-repeat sequence with seed 2 is almost the same, differing only in the last digit of each term (2 instead of 3 here). Indeed, any one-digit seed except 1 leads to essentially the same sequence with all terms identical except the last one = the seed.

Examples

			The term after 113 is obtained by saying (repeating) two two 1, one one 3, which gives 221113.

Crossrefs

Cf. A225329 (seed one), A225333 (seed two), A225332 (continuous look-and-repeat, seed 2), A225330, A225331 (continuous look-and-repeat, seed 1).
Cf. A005150 (original look-and-say), A225224, A221646, A225212 (continuous look-and-say versions).

Formula

a(n) = A225333(n) + 1.

A225298 Smallest pandigital number with exactly n prime factors (with multiplicity).

Original entry on oeis.org

10123457689, 10123456789, 1023456879, 1023456987, 1023456897, 1023456789, 1023456798, 1023457896, 1023486975, 1023479856, 1023458976, 1023475968, 1024973568, 1023579648, 1024897536, 1023657984, 1032984576, 1034698752, 1093865472, 1074659328, 1072963584
Offset: 1

Views

Author

Jonathan Vos Post, May 04 2013

Keywords

Comments

Smallest pandigital n-almost prime.

Examples

			a(1) = 10123457689 is the least prime pandigital number (A221646), that is, the smallest prime containing all the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
a(2) = 10123456789 = 919 * 11015731, the smallest pandigital semiprime.
a(3) = 1023456879, the smallest pandigital number (A171102) that is 3-almost prime (product of three primes with repetition).
a(4) = 1023456987 = 3^2 * 7 * 16245349, which is the smallest pandigital 4-almost prime.
a(5) = 1023456897 = 3^3 * 2417 * 15683.
a(6) = 1023456789 = 3^4 * 2221 * 5689.
a(7) = 1023456798 = 2 * 3^2 * 7 * 13 * 487 * 1283.
a(8) = 1023457896 = 2^3 * 3^3 * 59 * 80309.

Crossrefs

Cf. A171102, A221646, A175845.

Programs

  • Mathematica
    a[n_] := Block[{k = If[n < 3, 10123456789, 1023456789]}, While[ Union@ IntegerDigits@ k != Range[0, 9] || Total[Last /@ FactorInteger[k]] != n, k++]; k]; Array[a, 10] (* Giovanni Resta, May 06 2013 *)

Formula

a(n) = MIN{k such that k is in A050278 and bigomega(k) = n}.
a(n) = MIN{k such that k is in A050278 and A001222(k) = n}.

Extensions

a(2) corrected and a(9)-a(21) from Giovanni Resta, May 06 2013

A225335 A continuous "look-and-repeat" sequence (seed 3).

Original entry on oeis.org

3, 1, 1, 3, 2, 2, 1, 1, 1, 3, 2, 2, 2, 3, 3, 1, 1, 1, 3, 3, 3, 2, 2, 2, 3, 3, 3, 1, 3, 3, 3, 3, 3, 2, 3, 3, 3, 1, 1, 1, 5, 5, 3, 1, 1, 2, 3, 3, 3, 3, 3, 1, 2, 2, 5, 1, 1, 3, 2, 2, 1, 1, 1, 2, 5, 5, 3, 1, 1, 1, 2, 2
Offset: 1

Views

Author

Jean-Christophe Hervé, May 12 2013

Keywords

Comments

The 'look-and-repeat' sequence A225330, with seed 3. The variant A225331 with the same seed 3 gives this same sequence.
It describes at each step the preceding digits by repeating the frequency number.
The sequence is determined by triples of digits. The first two terms of a triple are the repeated frequency and the last term is the digit.
a(n) is always equal to 1, 2, 3, or 5. No series of four identical digits happens in the sequence, nor any of five 5's.
Applying the look-and-repeat principle to the sequence itself, it is simply shift one rank to the left.

Examples

			a(1) = 3, you then see "one 3" and repeating "one", a(2) = a(3) = 1 (one) and a(4) = 3; you have then two 1's, so 2,2,1 ; then one 3, so 1,1,3, etc.

Crossrefs

Cf. A225330, A225331 (two variants with seed 1), A225331 (seed 2), A225329, A225333, A225334 (look-and-repeat by block with resp. seed 1, seed 2, seed 3).
Cf. A005150 (original look-and-say), A225224, A221646, A225212 (continuous look-and-say versions).
Previous Showing 11-13 of 13 results.

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