A112063 -id:A112063 - cp's OEIS frontend

A112133 First differences of A112063.

1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1, 23, 1, 11, 13, 11, 1

Offset: 1

Antti Karttunen, Aug 28 2005

Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1).

Period=6. Also half of the first differences of A112073. Cf. A112086.

A112060 Square array A(x,y) = y-th natural number k for which A112049(k)=x and 0 if no such k exists; read by antidiagonals A(1,1), A(2,1), A(1,2), A(3,1), A(2,2), ...

Original entry on oeis.org

1, 2, 3, 5, 4, 11, 6, 7, 12, 24, 9, 8, 23, 35, 60, 10, 15, 36, 59, 155, 84, 13, 16, 47, 95, 275, 239, 144, 14, 19, 48, 119, 335, 575, 779, 180, 17, 20, 71, 120, 359, 659, 1499, 2855, 264, 18, 27, 72, 179, 419, 839, 1535, 4199, 5279, 420, 21, 28, 83, 204, 504

Offset: 1

Antti Karttunen, Aug 27 2005

This is a permutation of natural numbers provided that the sequence A112046 contains only prime values [which is true] and every prime occurs infinitely many times there.

			The top left corner of the array:
   1,  2,  5,  6,  9, 10, ...
   3,  4,  7,  8, 15, 16, ...
  11, 12, 23, 36, 47, ...

Index entries for sequences that are permutations of the natural numbers

A112070(x, y) = 2*A(X, Y)+1. Transpose: A112061. Column 1: A112051. Row 1: A042963, Row 2: A112062, Row 3: A112063, Row 4: A112064, Row 5: A112065, Row 6: A112066, Row 7: A112067, Row 8: A112068, Row 9: A112069.

Cf. also A227196.

A112073 Odd numbers n for which 5 is the smallest i (>= 1) with Jacobi symbol J(i,n) getting either a value 0 or -1.

Original entry on oeis.org

23, 25, 47, 73, 95, 97, 143, 145, 167, 193, 215, 217, 263, 265, 287, 313, 335, 337, 383, 385, 407, 433, 455, 457, 503, 505, 527, 553, 575, 577, 623, 625, 647, 673, 695, 697, 743, 745, 767, 793, 815, 817, 863, 865, 887, 913, 935, 937, 983, 985, 1007

Offset: 1

Antti Karttunen, Aug 27 2005

nonn

Row 3 of A112070. a(n) = 2*A112063(n)+1.

cp's OEIS Frontend

A112133 First differences of A112063.

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A112060 Square array A(x,y) = y-th natural number k for which A112049(k)=x and 0 if no such k exists; read by antidiagonals A(1,1), A(2,1), A(1,2), A(3,1), A(2,2), ...

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A112073 Odd numbers n for which 5 is the smallest i (>= 1) with Jacobi symbol J(i,n) getting either a value 0 or -1.

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