A048379 -id:A048379 - cp's OEIS frontend

A256296 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 0 to the digits of n written in base 6, then convert back to base 10.

1, 2, 3, 4, 5, 0, 13, 14, 15, 16, 17, 12, 19, 20, 21, 22, 23, 18, 25, 26, 27, 28, 29, 24, 31, 32, 33, 34, 35, 30, 1, 2, 3, 4, 5, 0, 79, 80, 81, 82, 83, 78, 85, 86, 87, 88, 89, 84, 91, 92, 93, 94, 95, 90, 97, 98, 99, 100, 101, 96

Offset: 0

M. F. Hasler, Mar 22 2015

Base 6 variant of A035327 (base 2) and A048379 (base 10). See A256293 - A256299 for bases 3 through 9, and A256306 for the variant where the result is not converted back to base 10.

			a(6) = 13 because 6 = 10[6] becomes 21[6] = 13.
a(35) = 0 because 35 = 55[6] becomes 00[6] = 0.

A256296(n,b=6)=!n+apply(t->(t+1)%b,n=digits(n,b))*vector(#n,i,b^(#n-i))~

A256297 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 0 to the digits of n written in base 7, then convert back to base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 0, 15, 16, 17, 18, 19, 20, 14, 22, 23, 24, 25, 26, 27, 21, 29, 30, 31, 32, 33, 34, 28, 36, 37, 38, 39, 40, 41, 35, 43, 44, 45, 46, 47, 48, 42, 1, 2, 3, 4, 5, 6, 0, 106, 107, 108, 109, 110, 111, 105, 113, 114, 115, 116

Offset: 0

M. F. Hasler, Mar 22 2015

Base 7 variant of A035327 (base 2) and A048379 (base 10). See A256293 - A256299 for bases 3 through 9, and A256307 for the variant where the result is not converted back to base 10.

			a(7) = 15 because 7 = 10[7] becomes 21[7] = 15.
a(48) = 0 because 48 = 66[7] becomes 00[7] = 0.

A256297(n,b=7)=!n+apply(t->(t+1)%b,n=digits(n,b))*vector(#n,i,b^(#n-i))~

A256305 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 0 to the digits of n written in base 5; do not convert back to base 10.

Original entry on oeis.org

1, 2, 3, 4, 0, 21, 22, 23, 24, 20, 31, 32, 33, 34, 30, 41, 42, 43, 44, 40, 1, 2, 3, 4, 0, 211, 212, 213, 214, 210, 221, 222, 223, 224, 220, 231, 232, 233, 234, 230, 241, 242, 243, 244, 240, 201, 202, 203, 204, 200, 311, 312, 313, 314, 310, 321, 322, 323

Offset: 0

M. F. Hasler, Mar 22 2015

Base 5 variant of A256078 (base 2) and A048379 (base 10). See A256303 - A256308 for bases 3 through 8, A256289 for base 9, and A256295 for the variant where the result is converted back to base 10.

			a(5) = 21 because 5 = "10" (in base 5) becomes "21".
a(24) = 0 because 24 = "44" (in base 5) becomes "00".

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Table[FromDigits[(IntegerDigits[n,5]+1/.(5->0))],{n,0,60}] (* Harvey P. Dale, Nov 15 2020 *)

A256305(n,b=5)=!n+eval(Strchr(apply(d->(d+1)%b+48, digits(n,b))))

A256306 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 0 to the digits of n written in base 6; do not convert back to base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 0, 21, 22, 23, 24, 25, 20, 31, 32, 33, 34, 35, 30, 41, 42, 43, 44, 45, 40, 51, 52, 53, 54, 55, 50, 1, 2, 3, 4, 5, 0, 211, 212, 213, 214, 215, 210, 221, 222, 223, 224, 225, 220, 231, 232, 233, 234, 235, 230, 241, 242, 243, 244, 245, 240

Offset: 0

M. F. Hasler, Mar 22 2015

Base 6 variant of A256078 (base 2) and A048379 (base 10). See A256303 - A256308 for bases 3 through 8, A256289 for base 9, and A256296 for the variant where the result is converted back to base 10.

			a(6) = 21 because 6 = "10" (in base 6) becomes "21".
a(35) = 0 because 35 = "55" (in base 6) becomes "00".

A256306(n,b=6)=!n+eval(Strchr(apply(d->(d+1)%b+48, digits(n,b))))

A270388 a(n) = A048739(n-2) mod n.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 3, 1, 0, 8, 0, 1, 8, 0, 0, 13, 0, 8, 17, 1, 0, 0, 20, 1, 21, 8, 0, 19, 0, 0, 3, 1, 34, 8, 0, 1, 29, 8, 0, 7, 0, 8, 41, 1, 0, 0, 21, 31, 3, 8, 0, 13, 9, 8, 3, 1, 0, 20, 0, 1, 59, 0, 20, 49, 0, 8, 26, 1, 0, 0, 0, 1, 3, 8, 20, 49, 0, 48, 75, 1, 0, 56, 20, 1, 32, 24, 0, 49, 28, 8, 65, 1, 39, 0, 0, 85, 3, 68, 0

Offset: 2

Altug Alkan, Mar 16 2016

nonn

If n is an odd prime, a(n) = 0. In other words, ((1-sqrt(2))^p + (1+sqrt(2))^p - 2) is divisible by p where p is an odd prime.

Cf. A000129, A048739.

a048379(n) = my(w=quadgen(8));-1/2+(3/4+1/2*w)*(1+w)^n+(3/4-1/2*w)*(1-w)^n;
a(n) = a048379(n-2) % n;

a(n) = (((1-sqrt(2))^n + (1+sqrt(2))^n - 2) / 4) mod n, for n > 1.

cp's OEIS Frontend

A256296 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 0 to the digits of n written in base 6, then convert back to base 10.

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A256297 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 0 to the digits of n written in base 7, then convert back to base 10.

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A256305 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 0 to the digits of n written in base 5; do not convert back to base 10.

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A256306 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 0 to the digits of n written in base 6; do not convert back to base 10.

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A270388 a(n) = A048739(n-2) mod n.

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