C (GCC), 63 bytes

i;main(j){for(;;~j%7%3||printf("%d ",i))for(j=++i;j%7<1;)j/=7;}

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Port of @m90's answer

C (gcc), ⁸² 74 bytes

-8 bytes thanks to @Digital Trauma

i;main(j,k){for(;;k%3||printf("%d ",i))for(k=ffs(j=++i)-1;j%3<1;j/=3)k--;}

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Port of @math scat's answer

C (GCC), 63 bytes

i;main(j){for(;;~j%7%3||printf("%d ",i))for(j=++i;j%7<1;)j/=7;}

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Port of @m90's answer

C (gcc), ⁸² 74 bytes

-8 bytes thanks to @Digital Trauma

i;main(j,k){for(;;k%3||printf("%d ",i))for(k=ffs(j=++i)-1;j%3<1;j/=3)k--;}

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Port of @math scat's answer

C (GCC), 63 bytes

i;main(j){for(;;~j%7%3||printf("%d ",i))for(j=++i;j%7<1;)j/=7;}

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Port of @m90's answer

C (gcc), 82 bytes

i;main(j,k){for(;;k%3||printf("%d ",i))for(k=__builtin_ctz(j=++i);j%3<1;j/=3)k--;}

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Port of @math scat's answer

C (GCC), 63 bytes

i;main(j){for(;;~j%7%3||printf("%d ",i))for(j=++i;j%7<1;)j/=7;}

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Port of @m90's answer

C (gcc), ⁸² 74 bytes

-8 bytes thanks to @Digital Trauma

i;main(j,k){for(;;k%3||printf("%d ",i))for(k=ffs(j=++i)-1;j%3<1;j/=3)k--;}

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Port of @math scat's answer

C (gcc), 82 bytes

i;main(j,k){for(;;k%3||printf("%d ",i))for(k=__builtin_ctz(j=++i);j%3<1;j/=3)k--;}

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Port of @math scat's answer

C (GCC), 63 bytes

i;main(j){for(;;~j%7%3||printf("%d ",i))for(j=++i;j%7<1;)j/=7;}

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Port of @m90's answer

C (gcc), 82 bytes

i;main(j,k){for(;;k%3||printf("%d ",i))for(k=__builtin_ctz(j=++i);j%3<1;j/=3)k--;}

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Port of @math scat's answer