A102850 Non-monotonic "True so far" sequence: In the first n terms, the digit (a(n) mod 10) occurs floor(a(n)/10) times; a(n) is the smallest such number.

10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 34, 35, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 56, 57, 58, 59, 60, 67, 68, 69, 70, 78, 79, 80, 89, 90, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124

Offset: 1

Author

David Wasserman, Feb 28 2005

Keywords

• base
• easy
• fini
• nonn
• less

Comments

Sequence has 5191475 terms. The numbers of occurrences of digits 0-9 are 3589309, 4812817, 4977431, 4564762, 3741602, 3738734, 3599425, 3599878, 3598956, 3589537.

This sequence first differs from the original "True so far" sequence A102357 at a(351) = 920 because this is the first term that is less than the previous term, 1002.

The sequence is injective (no term appears twice) as consequence of the definition, while this is imposed through monotonicity in A102357. - M. F. Hasler, Nov 18 2019

Examples

			a(10) = 20 because up to this point there are two 0 digits in the sequence, including the 0 in 20.
a(5191476) doesn't exist. 35893100 would yield a total of 3589311 0's, while 35893110 or 35893120 would yield 3589310 0's. Similar reasons prevent other terms ending with other digits.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..10000, Nov 18 2019

Crossrefs

Cf. A102357.

Programs

PARI

c=Vec(0,10); for(n=1,351, a=vecmin(c)*10+10; while(a\10<=c[a%10+1] || a\10 != c[a%10+1]+#select(d->d==a%10,digits(a)), a++); [c[d+1]++|d<-digits(a)]; print1(a",")) \\ M. F. Hasler, Nov 18 2019