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A163556 Composite numbers such that exactly four distinct permutations of decimal digits are prime. 3
170, 194, 710, 790, 791, 793, 914, 917, 970, 973, 1003, 1012, 1015, 1016, 1024, 1028, 1030, 1042, 1082, 1090, 1102, 1105, 1106, 1120, 1126, 1135, 1138, 1150, 1157, 1159, 1160, 1162, 1175, 1178, 1183, 1195, 1204, 1208, 1210, 1216, 1234, 1240, 1243, 1258 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 170 because 170 is composite, the four permutations 17, 71, 107, and 701 are all prime, and no other permutation of 170 is prime.

MAPLE

filter:= proc(n) local d, Permutor, P, c, i;

  if isprime(n) then return false fi;

  d:= ilog10(n)+1;

  Permutor:= Iterator:-Permute(convert(n, base, 10));

  c:= 0;

  for P in Permutor do

    if isprime(add(P[i]*10^(i-1), i=1..d)) then

      c:= c+1;

      if c >= 5 then return false fi;

    fi

  od;

  evalb(c=4)

end proc:

select(filter, [$10..2000]); # Robert Israel, Aug 10 2020

MATHEMATICA

Select[Range[1300], CompositeQ[#]&&Count[FromDigits/@Permutations[ IntegerDigits[ #]], _?PrimeQ]==4&] (* Harvey P. Dale, Oct 26 2015 *)

CROSSREFS

Cf. A163554, A163555, A163557, A163558, A163559, A163560, A163561, A163562.

Sequence in context: A043658 A296892 A045002 * A229467 A218071 A113789

Adjacent sequences:  A163553 A163554 A163555 * A163557 A163558 A163559

KEYWORD

easy,nonn,base

AUTHOR

Gil Broussard, Jul 30 2009

STATUS

approved

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Last modified January 26 19:15 EST 2022. Contains 350599 sequences. (Running on oeis4.)