A321513 -id:A321513 - cp's OEIS frontend

A352966 Primes of the form A321513(k) + 1 for some k > 0.

11, 43, 103, 131, 137, 239, 521, 547, 683, 911, 1093, 1171, 1301, 1543, 1951, 2081, 2341, 2731, 2861, 3121, 3251, 3511, 3823, 6151, 9767, 12301, 13879, 16963, 17477, 18451, 20047, 21589, 23131, 24967, 26729, 30841, 32771, 32801, 33289, 34439, 36901, 40093

Offset: 1

Felix Fröhlich, Apr 12 2022

Contains the two known Wieferich primes (A001220), i.e., 1093 and 3511.

Is A001220 a subsequence?

			1543 is prime and 1542 is 120012 in base 4, which is 00120012 when leading zeros are added and thus periodic, so 1543 is a term of the sequence.

Cf. A001220, A321513.

is(n, b=4) = for (w=1, oo, my (d=digits(n, b^w)); if (#d<=1, return (0), #Set(d)==1, return (1))) \\ after Rémy Sigrist in A321513
forprime(p=1, 1e5, if(is(p-1), print1(p, ", ")))

A353339 Number of integers b with n > b > 1 such that the base-b representation of n is periodic.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 2, 2, 4, 1, 2, 2, 2, 3, 2, 3, 4, 1, 3, 4, 2, 1, 4, 1, 4, 3, 4, 1, 4, 3, 3, 3, 4, 2, 5, 2, 2, 2, 5, 1, 5, 2, 3, 4, 2, 1, 5, 1, 5, 4, 4, 1, 5, 2, 4, 3, 2, 1, 7, 1, 3, 5, 3, 5, 5, 1, 5, 2, 5, 1, 5, 3, 3, 3, 3, 2, 5, 1, 6, 2, 4, 1, 7, 4, 3, 2

Offset: 1

Felix Fröhlich, Apr 14 2022

			For n = 10: The base-2, base-3, base-4 and base-9 representations of 10 are 1010, 0101, 22 and 11, respectively, and these are the only representations that are periodic, so a(10) = 4.

Cf. A121016, A242138, A242139, A321513.

is(n, b) = for (w=1, oo, my (d=digits(n, b^w)); if (#d<=1, return (0), #Set(d)==1, return (1))) \\ after Rémy Sigrist in A321513
a(n) = my(i=0); for(b=2, n-1, if(is(n, b), i++)); i

A353340 Smallest positive number k such that there are exactly n integers b with k > b > 1 where the base-b representation of k is periodic.

Original entry on oeis.org

1, 3, 5, 15, 10, 36, 80, 60, 120, 168, 260, 252, 360, 630, 504, 720, 840, 1512, 1260, 1800, 1680, 2340, 3276, 3120, 3360, 2520, 9072, 7200, 6300, 12096, 7920, 5040, 9240, 7560, 20520, 25920, 15840, 10080

Offset: 0

Felix Fröhlich, Apr 14 2022

Cf. A353339.

is(n, b) = for (w=1, oo, my (d=digits(n, b^w)); if (#d<=1, return (0), #Set(d)==1, return (1))) \\ after Rémy Sigrist in A321513
a353339(n) = my(i=0); for(b=2, n-1, if(is(n, b), i++)); i
a(n) = for(k=1, oo, if(a353339(k)==n, return(k)))

cp's OEIS Frontend

A352966 Primes of the form A321513(k) + 1 for some k > 0.

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A353339 Number of integers b with n > b > 1 such that the base-b representation of n is periodic.

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PARI

A353340 Smallest positive number k such that there are exactly n integers b with k > b > 1 where the base-b representation of k is periodic.

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Author

Keywords

Crossrefs

Programs

PARI