cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A381661 Primes p such that the first period of the decimal expansion of 1 / p contains no digits of p as many times they are contained in p.

This page as a plain text file.
%I A381661 #23 Mar 04 2025 15:21:19
%S A381661 2,5,11,13,37,41,67,73,79,101,137,211,239,271,353,2161,4649,8779,
%T A381661 16763,21401,21649,25601,27961,52579,123551,333667,513239,538987,
%U A381661 1676321
%N A381661 Primes p such that the first period of the decimal expansion of 1 / p contains no digits of p as many times they are contained in p.
%e A381661 p = 2: 1/2 = 0.500..., the period contains no 2, thus 2 is a term.
%e A381661 p = 13: 1/13 = 0.076923..., the period contains no one 1 AND one 3, thus 13 is a term.
%e A381661 P = 211: 1/211 = 0.004739336492890995260663507109..., the period contains no one 2 AND two 1's, thus 211 is a term.
%t A381661 q[p_] := Module[{r = Range[0, 9]}, !AllTrue[Count[RealDigits[1/p][[1, -1]], #] & /@ r - DigitCount[p, 10, r], # >= 0 &]]; Select[Prime[Range[1000]], q] (* _Amiram Eldar_, Mar 03 2025 *)
%Y A381661 Cf. A000040, A006559, A186641.
%K A381661 nonn,base,more
%O A381661 1,1
%A A381661 _Ctibor O. Zizka_, Mar 03 2025
%E A381661 a(16)-a(28) from _Amiram Eldar_, Mar 03 2025
%E A381661 a(29) from _Chai Wah Wu_, Mar 04 2025