A112065 -id:A112065 - cp's OEIS frontend

A112135 First differences of A112065.

95, 120, 60, 24, 60, 85, 60, 36, 95, 60, 145, 84, 11, 25, 59, 36, 84, 60, 1, 155, 25, 84, 71, 24, 60, 1, 144, 95, 25, 71, 24, 61, 84, 71, 25, 59, 25, 71, 84, 61, 24, 71, 25, 95, 144, 1, 60, 24, 71, 84, 25, 155, 1, 60, 84, 36, 59, 25, 11, 84, 145, 60, 95, 36, 60, 85

Offset: 1

Antti Karttunen, Aug 28 2005

nonn

Period=72. Also half of the first differences of A112075. 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.

A112075 Odd numbers n for which 11 is the smallest i (>= 1) with Jacobi symbol J(i,n) getting either a value 0 or -1.

Original entry on oeis.org

121, 311, 551, 671, 719, 839, 1009, 1129, 1201, 1391, 1511, 1801, 1969, 1991, 2041, 2159, 2231, 2399, 2519, 2521, 2831, 2881, 3049, 3191, 3239, 3359, 3361, 3649, 3839, 3889, 4031, 4079, 4201, 4369, 4511, 4561, 4679, 4729, 4871, 5039, 5161

Offset: 1

Antti Karttunen, Aug 27 2005

nonn

Row 5 of A112070. a(n) = 2*A112065(n)+1.

cp's OEIS Frontend

A112135 First differences of A112065.

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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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A112075 Odd numbers n for which 11 is the smallest i (>= 1) with Jacobi symbol J(i,n) getting either a value 0 or -1.

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