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A292569 Least pandigital number which sums up with the n-th pandigital number A171102(n) to another pandigital number. 1
1023456789, 1023456789, 1023456879, 1023456978, 1023456879, 1023456798, 1023457689, 1023457689, 1023457869, 1023459687, 1023457869, 1023459867, 1023458679, 1023459678, 1023458769, 1023456987, 1023459768, 1023456897, 1023458679, 1023457698, 1023458769 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 23:41 EST 2020. Contains 332113 sequences. (Running on oeis4.)