A359356 -id:A359356 - cp's OEIS frontend

A359517 Inverse permutation (conjectured) of A359356.

0, 1, 80, 204, 241, 1220, 1647, 862, 1248, 481, 2, 603, 3, 70, 22, 13, 49, 42, 121, 67, 79, 36, 925, 132, 122, 95, 59, 94, 165, 101, 203, 16, 38, 2396, 244, 169, 343, 344, 140, 174, 240, 28, 81, 116, 2179, 246, 149, 266, 864, 247, 1219, 46, 54, 18, 229, 27492

Offset: 0

M. F. Hasler, Jan 03 2023

			a(55) = 27492 because A359356(27492) = 55.

Alois P. Heinz, Table of n, a(n) for n = 0..554

Cf. A359356.

def A359517(n, i=0):
    while A359356(i) != n: i += 1
    return i

A359256 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number which has not appeared such that all the distinct prime factors of a(n-1) + a(n) are factors of a(n).

Original entry on oeis.org

1, 2, 6, 3, 24, 8, 56, 42, 7, 336, 48, 16, 112, 84, 12, 4, 28, 21, 60, 15, 10, 22, 66, 30, 18, 9, 72, 36, 45, 80, 20, 5, 120, 40, 85, 204, 39, 78, 26, 38, 90, 35, 14, 50, 75, 150, 93, 186, 57, 114, 102, 34, 94, 162, 54, 27, 216, 108, 135, 240, 144, 99, 198, 44, 77, 266, 95, 380, 132, 110, 11

Offset: 1

Scott R. Shannon and Eric Angelini, Jan 05 2023

nonn

The primes do not occur in their natural order, and for all terms studied if a(n) is a prime p, then a(n-1) = p(p-1) and a(n+1) = p(p^2-1). In the first 10000 terms the fixed points are 22, 165, 710, 1005, 9003, although it is likely more exist. The sequence is conjectured to be a permutation of the positive integers.

			a(3) = 6 as a(2) + 6 = 2 + 6 = 8 which has 2 as its only distinct prime factor, and 2 is a factor of 6.
a(8) = 42 as a(7) + 42 = 56 + 42 = 96 which has 2 and 3 as distinct prime factors,  and 2 and 3 are factors of 42.
a(10) = 336 as a(9) + 336 = 7 + 336 = 343 which has 7 as its only distinct prime factor, and 7 is a factor of 336. Note that 336 = 7(7^2-1).

Scott R. Shannon, Table of n, a(n) for n = 1..10000.

Cf. A359557, A027748, A359356, A064413, A352867.

cp's OEIS Frontend

A359517 Inverse permutation (conjectured) of A359356.

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