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A187016 Seven-digit primes with derangement of digits 1..7. 1
2365471, 2375641, 2456371, 2456731, 2457613, 2467351, 2476351, 2516473, 2547613, 2547631, 2561743, 2576341, 2645371, 2651743, 2653741, 2657143, 2657341, 2716453, 2741653, 2761453, 2765143, 3452671, 3456721, 3462751, 3465271, 3467251, 3526741, 3546271, 3546721, 3576421, 3627451, 3672451, 3675241, 3752641, 3756241, 3756421 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No digit is on its "right" place. There are exactly 143 such primes.

The only another possible case: four-digit primes with a derangement of digits 1..4 gives two primes 2143, 2341. There are no such primes with m=1,2,3,5,6,8,9 decimal digits 1..m.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..143 (complete list)

EXAMPLE

2365471 is prime and 2 is not at 2nd place, 3 - not at 3rd place, 6 - not at 6th place, ..., 1 - not at the first place. Largest such prime is a(143)=7652413.

MATHEMATICA

derangQ[n_]:=Count[Thread[{n, Range[7]}], _?(#[[1]]==#[[2]]&)]==0; With[ {p7=Permutations[Range[7]]}, Select[p7, derangQ[#]&&PrimeQ[ FromDigits[ #]]&]] (* Harvey P. Dale, Sep 28 2017 *)

CROSSREFS

Cf. A000166.

Sequence in context: A204944 A184771 A210075 * A237487 A236484 A167438

Adjacent sequences:  A187013 A187014 A187015 * A187017 A187018 A187019

KEYWORD

nonn,base,fini,full

AUTHOR

Zak Seidov, Mar 01 2011

STATUS

approved

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)