A381419 -id:A381419 - cp's OEIS frontend

A381821 Fixed points of A381419.

1, 81, 91, 93, 110, 122, 129, 156, 159, 163, 165, 172, 185, 188, 201, 205, 213, 216, 232, 254, 281, 286, 292, 356, 481, 507, 548, 3553, 3698, 3776, 3796, 3808, 3909, 4132, 4199, 4250, 4318, 4414, 4712, 4713, 4805, 4898, 4912, 4976, 5005, 5182, 5193, 5354, 5361, 5445, 5577, 5658, 5696

Offset: 1

Scott R. Shannon, Mar 07 2025

nonn

Scott R. Shannon, Table of n, a(n) for n = 1..741

Cf. A381419, A381420.

A381420 a(1) = 1, a(2) = 3; for n > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) and has a different binary weight than a(n-1).

Original entry on oeis.org

1, 3, 15, 5, 25, 10, 2, 6, 4, 12, 8, 14, 16, 18, 21, 9, 27, 24, 22, 20, 26, 30, 28, 32, 34, 38, 36, 39, 13, 65, 35, 40, 42, 33, 11, 55, 44, 46, 48, 45, 50, 54, 52, 58, 56, 60, 62, 64, 66, 51, 17, 85, 68, 70, 63, 7, 77, 49, 91, 78, 69, 23, 115, 75, 72, 57, 19, 95, 76, 80, 74, 86, 82, 90

Offset: 1

Scott R. Shannon, Feb 23 2025

Unlike the EKG sequence A064413 the primes do not appear in their natural order. The only fixed points in the terms studied are 1 and 20, and it is likely no more exist. The sequence is conjectured to be a permutation of the positive integers.

			a(4) = 5 as a(3) = 15 which shares a factor with 5 while the binary weight of 5 (101_2) is 2 while the binary weight of 15 (1111_2) is 4.

Scott R. Shannon, Table of n, a(n) for n = 1..10000
Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Cf. A381419, A000120, A109451, A064413, A093714, A027748.

lista(n)= my(i=1, j=0, r=Vec([1], n), s=List(), u=1); while(iRuud H.G. van Tol, Mar 10 2025

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A381821 Fixed points of A381419.

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A381420 a(1) = 1, a(2) = 3; for n > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) and has a different binary weight than a(n-1).

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