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A330286 Tally the digits of n: list the distinct digits of n in order of appearance, each followed by the respective count, concatenate. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 12:23 EDT 2021. Contains 348041 sequences. (Running on oeis4.)