A248651 a(n) is the smallest number greater than a(n-1) such that in a(1) through a(n) no digit occurs more than once more than any other digit, starting with a(1) = 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 34, 56, 78, 79, 80, 91, 234, 256, 301, 456, 789, 790, 812, 3456, 3457, 6012, 6089, 7123, 8459, 8460, 9123, 9157, 20345, 20678, 31456, 31789, 40256, 40789, 51236, 51789, 60234, 60789, 71234, 71589, 80234, 80569, 91234, 91567, 203456, 203478, 516789, 516790, 518234, 602347, 602389, 714589, 714590, 716238, 802345, 802369, 914567, 914568, 917023, 2034567

Offset: 1

Author

Jeb Adams, Oct 10 2014

Keywords

• nonn
• base

Comments

Starting with 1, instead of 0 as in A095204, means 0 doesn't appear until a(10)=10, hence a(11)=20, not 23.

Links

• Jeb Adams, Table of n, a(n) for n = 1..300

Crossrefs

Same definition of A095204, but starting with 1. Similar to A120125.

Programs

R

# Script (R, using base only) to build values in the sequence defined
# in A248651:
# a(n) is the smallest number greater than a(n-1) such that no
# digit appears in the listing of all terms more than one time
# more than any other digit in the listing, with a(1) = 1.
digits <- c(0:9) #vector of the digits
digitCounts <- rep(0L,10) #vector for digit count tracking
A <- c() #vector of entries
A[1] <- 1L #first entry
failed <- 1L #failed entry
digitCounts[2] = 1L #impact of first entry on digitCounts
# Build a function that turns a number into a vector of its
# component digits
digits <- function(x) {
  if(length(x) > 1 ) {
    lapply(x, digits)
  } else {
    n <- floor(log10(x))+1L
    rev( x %/% 10^seq(0, length.out=n) %% 10 )
  }
}
# Engine for testing digits, runs VERY SLOW, but checks every integer.
# I welcome improvements, note that it respects incrementing
# more than one digit at a time if that makes sense.
while (length(A) < 300) {
  i <- max(failed, max(A)) + 1
  newCounts <- digitCounts
  digitList <- digits(i)
  for (j in digitList) {
    newCounts[j + 1] <- newCounts[j + 1] + 1
  }
  if (max(newCounts) - min(newCounts) > 1) {
       failed <- i } else {
        digitCounts <- newCounts
        A <- c(A,as.integer(i))
      }
} # Jeb Adams, Jul 17 2020

Extensions

Terms a(15) and beyond corrected by Jeb Adams, May 01 2020