A292569 Least pandigital number which sums up with the n-th pandigital number A171102(n) to another pandigital number.

1023456789, 1023456789, 1023456879, 1023456978, 1023456879, 1023456798, 1023457689, 1023457689, 1023457869, 1023459687, 1023457869, 1023459867, 1023458679, 1023459678, 1023458769, 1023456987, 1023459768, 1023456897, 1023458679, 1023457698, 1023458769

Offset

1,1

Comments

The first 9*9! pandigital numbers (having each digit 0-9 exactly once) are listed in A050278, which is extended to the infinite sequence A171102 of pandigital numbers having each digit 0-9 at least once.

For all n, a(n) is well defined, because to any pandigital number N = A171102(n) we can add the number M(N) = 123456789*10^k with k = # digits of N, which is pandigital (in the above extended sense) as well as is the sum N + M(N) (equal to the concatenation of 123456789 and N). In practice, there are much smaller solutions. We conjecture that there is always a 10-digit solution a(n) < 10^10.

Links

Table of n, a(n) for n=1..21.

Formula

a(n) = A171102(A292570(n)).

a(n) = min { N in A171102 | N + A171102(n) in A171102 }.

Example

The smallest pandigital number A171102(1) = A050278(1) = 1023456789, added to itself, yields again a pandigital number, 2046913578. Therefore, a(1) = A171102(1) = 1023456789.
Similarly, A171102(1) = 1023456789, added to the second pandigital number A171102(2) = 1023456798, yields the pandigital number 2046913587. Therefore also a(2) = A171102(1) = 1023456789.
Considering the third pandigital number A171102(3) = 1023456879, we have to add itself in order to get a pandigital number, 2046913758. (Adding A171102(1) or A171102(2) yields 2046913668 and 2046913677, respectively, which are not pandigital.) Therefore a(3) = A171102(3) = 1023456879.

Prog

(PARI) a(n)={n=A171102(n); for(k=1, 9e9, #Set(digits(n+A171102(k)))>9&&return(A171102(k)))} \\ For illustrational purpose only; not optimized for efficiency.

Crossrefs

Cf. A292570 (index of a(n) within A171102), A171102, A050278.

Sequence in context: A074205 A277054 A218770 * A204045 A061604 A302096

Adjacent sequences: A292566 A292567 A292568 * A292570 A292571 A292572

Keyword

nonn,base

Author

M. F. Hasler, Sep 19 2017

Status

approved