A330286 Tally the digits of n: list the distinct digits of n in order of appearance, each followed by the respective count, concatenate.

1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 1101, 12, 1121, 1131, 1141, 1151, 1161, 1171, 1181, 1191, 2101, 2111, 22, 2131, 2141, 2151, 2161, 2171, 2181, 2191, 3101, 3111, 3121, 32, 3141, 3151, 3161, 3171, 3181, 3191, 4101, 4111, 4121, 4131, 42, 4151, 4161, 4171, 4181, 4191, 5101, 5111

Offset

0,2

Comments

The term a(0) = 1 means 01 without the leading zero; no other number is affected by this problem of the leading zero.

Similar to the "Look & Say" operation LS = A045918, in which the count precedes the digit. However, here each distinct digit is considered only once: Thus, while LS(121) = 111211, a(121) = 1221 ("digit 1 twice, digit 2 once").

Links

Table of n, a(n) for n=0..51.

Formula

If n is in A010784 (has only distinct digits), then a(n) = (n with an additional digit 1 inserted after each digit).

Example

a(1) = 11 for "digit 1, once".
a(10) = 1101 for "digit 1, once; digit 0, once".
a(11) = 12 for "digit 1, twice".
a(12) = 1121 for "digit 1, once; digit 2, once".
a(100) = 1102 for "digit 1, once; digit 0, twice".a(111) = 13, for "digit 1, three times".

Mathematica

A330286[n_] := FromDigits@ Flatten@ IntegerDigits@ Flatten@ Tally@ IntegerDigits[n];
Table[A330286[n], {n, 0, 50}]

Prog

(PARI) apply( a(n)={eval(concat(vector(#n=digits(n), i, if(!setsearch(Set(n[1..i-1]), n[i]), Str(n[i], #select(d->d==n[i], n)), ""))))}, [1..111])

Crossrefs

Cf. A045918 (look and say), A010784.

Sequence in context: A017281 A061589 A110402 * A081927 A181178 A178205

Adjacent sequences: A330283 A330284 A330285 * A330287 A330288 A330289

Keyword

nonn,base,less

Author

M. F. Hasler, Dec 09 2019

Status

approved