A112069 -id:A112069 - cp's OEIS frontend

A112139 First differences of A112069.

5015, 2616, 9240, 2844, 5496, 1140, 325, 5639, 2220, 6636, 1465, 420, 719, 420, 1560, 265, 2675, 2041, 5939, 1621, 3035, 2664, 336, 769, 3791, 1980, 949, 4211, 2329, 755, 2941, 839, 145, 635, 2665, 71, 420, 204, 216, 685, 1824, 3060, 420, 731

Offset: 1

Antti Karttunen, Aug 28 2005

nonn

Half of the first differences of A112079. 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.

A112079 Odd numbers k for which 23 is the smallest positive i with Jacobi symbol J(i,k) != 1.

Original entry on oeis.org

529, 10559, 15791, 34271, 39959, 50951, 53231, 53881, 65159, 69599, 82871, 85801, 86641, 88079, 88919, 92039, 92569, 97919, 102001, 113879, 117121, 123191, 128519, 129191, 130729, 138311, 142271, 144169, 152591, 157249, 158759, 164641, 166319, 166609, 167879

Offset: 1

Antti Karttunen, Aug 27 2005

nonn

Andy Huchala, Table of n, a(n) for n = 1..20000

Row 9 of A112070.

a(n) = 2*A112069(n) + 1.

ls = []
for c in range(1, 10^5, 2):
    for i in range(1, 24):
        if jacobi_symbol(i, c) <= 0:
            if i < 23:
                break
            else:
                ls.append(c)
print(ls) # Andy Huchala, Feb 11 2023

a(31)-a(35) from Andy Huchala, Feb 10 2023

Name simplified by Sean A. Irvine, Feb 25 2023

cp's OEIS Frontend

A112139 First differences of A112069.

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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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A112079 Odd numbers k for which 23 is the smallest positive i with Jacobi symbol J(i,k) != 1.

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