A140057 -id:A140057 - cp's OEIS frontend

A113589 A complementary variation of 'n described': if n is read as "a ones b twos" then a(n) = "one a's two b's", etc.

0, 1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1, 2, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11, 111, 22, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111, 1111, 11111, 222

Offset: 0

Amarnath Murthy, Nov 07 2005

			A045918(10) = 1110 = 'one one one zero', hence a(10) = 'one one, zero ones' = 1.
A045918(11) = 21 = 'two ones', hence a(11) = 'one twos' = 2.
a(123) = 111111.

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Cf. A002275, A045918, A140057, A306366.

a(n) = { my (d=[]); while (n, my (t=n%10, k=0); while (n%10==t, n\=10; k++;); for (i=1, t, d=concat(digits(k), d))); fromdigits(d) } \\ Rémy Sigrist, Feb 09 2022

a(A002275(n)) = n. - Rémy Sigrist, Feb 09 2022

Extended and corrected by Nathaniel Johnston, Apr 29 2011

a(0) = 0 prepended by Rémy Sigrist, Feb 09 2022

A165411 Primes p such that each of p's digits d appears consecutively exactly d times and p contains each nonzero digit up to its maximum digit.

Original entry on oeis.org

223331, 122555554444333, 224444333555551, 224444555553331, 225555544441333, 333555554444221, 555552233344441, 555552244441333, 555554444221333, 122444455555666666333, 122555554444666666333, 144446666662255555333

Offset: 1

Rick L. Shepherd, Sep 17 2009

This sequence is a subsequence of A140057, A078348, and A108571. There are 129 terms; the largest is 7777777666666444455555223331. As 1, 122, and 221 are not prime and any such numbers whose maximum digit is 4, 8, or 9 are divisible by 3, all terms of the sequence have either 6 (1 term), 15 (8 terms), 21 (24 terms), or 28 (96 terms) decimal digits (=triangular numbers A000217(n) for n=3,5,6,7, respectively).

None of the terms have nondecreasing or nonincreasing decimal digits. - Rick L. Shepherd, Feb 23 2013

			1333444455555226666667777777 is a term because it is a prime meeting the criteria: It contains all digits 1 through 7, its maximum, each appearing in a single run of length equal to the value of the digit.

Rick L. Shepherd, Table of n, a(n) for n = 1..129 (full sequence)

Cf. A140057, A078348, A108571.

cp's OEIS Frontend

A113589 A complementary variation of 'n described': if n is read as "a ones b twos" then a(n) = "one a's two b's", etc.

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