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.
2, 5, 11, 13, 37, 41, 67, 73, 79, 101, 137, 211, 239, 271, 353, 2161, 4649, 8779, 16763, 21401, 21649, 25601, 27961, 52579, 123551, 333667, 513239, 538987, 1676321
Offset: 1
Examples
p = 2: 1/2 = 0.500..., the period contains no 2, thus 2 is a term. p = 13: 1/13 = 0.076923..., the period contains no one 1 AND one 3, thus 13 is a term. P = 211: 1/211 = 0.004739336492890995260663507109..., the period contains no one 2 AND two 1's, thus 211 is a term.
Programs
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Mathematica
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 *)
Extensions
a(16)-a(28) from Amiram Eldar, Mar 03 2025
a(29) from Chai Wah Wu, Mar 04 2025