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 A343823 Numbers k > 10 such that every permutation of the digits of k is congruent to 3 (mod 4). 0

%I #6 May 09 2021 10:05:02

%S 11,15,19,51,55,59,91,95,99,111,115,119,151,155,159,191,195,199,511,

%T 515,519,551,555,559,591,595,599,911,915,919,951,955,959,991,995,999,

%U 1111,1115,1119,1151,1155,1159,1191,1195,1199,1511,1515,1519,1551,1555,1559

%N Numbers k > 10 such that every permutation of the digits of k is congruent to 3 (mod 4).

%C Also numbers that contain only the digits 1,5,9. More general : Numbers k > 10 such that every permutation of the digits of k is congruent to r (mod m). For m = 4; r = 0 gives A343810, r = 1 gives A143967, r = 2 gives A284632, r = 3 gives this sequence.

%e 159 = 4*39 + 3, 195 = 4*48 + 3, 519 = 4*104 + 3, 591 = 4*147 + 3, 915 = 4*228 + 3, 951 = 4*237 + 3.

%t Select[Range[11, 1600], AllTrue[Permutations[IntegerDigits[#]], Mod[FromDigits[#1], 4] == 3 &] &] (* _Amiram Eldar_, Apr 30 2021 *)

%Y Cf. A143967, A284632, A343810.

%K nonn,base,easy

%O 11,1

%A _Ctibor O. Zizka_, Apr 30 2021

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Last modified August 15 13:43 EDT 2024. Contains 375173 sequences. (Running on oeis4.)