A260310 -id:A260310 - cp's OEIS frontend

A260408 Bisection of A260310.

3, 7, 11, 7, 17, 29, 41, 53, 31, 71, 29, 107, 61, 41, 131, 53, 157, 113, 179, 239, 131, 79, 73, 127, 127, 229, 223, 113, 199, 73, 317, 181, 43, 269, 241, 89, 193, 101, 89, 211, 331, 167, 313, 409, 97, 113, 401, 480, 193, 109, 457, 241, 431

Offset: 1

Robert G. Wilson v, Jul 24 2015

nonn

Lesser (member) of the n-th pair in A260310.
Most of the terms are prime, 97.25%, but there are composites, 2.75%: 480, 960, 990, 1200, 1170, 1950, 1890, 2610, ..., . They seem to all be congruent 0 (mod 6).
Conjecture: when a(n) is prime, A260409(n) is composite and vice versa. No contradictions in the first 10000 terms.
A260408 sorted without repeats: 3, 7, 11, 17, 29, 31, 41, 43, 53, 61, 71, 73, 79, 89, 97, 101, ..., .
Primes that have not appeared yet (10000 terms examined): 2, 5, 13, 19, 23, 37, 47, 59, 67, 83, 103, 139, 151, 163, 191, 197, ..., .

			See A260310.

Robert G. Wilson v, Table of n, a(n) for n = 1..9906

Cf. A260310, A260409, A260410.

(* first run the Mmca in A260310 and then *) Take[ Transpose[ lst][[1]], 75]

a(n) = A260310(2n-1).

A260409 Bisection of A260310.

Original entry on oeis.org

8, 16, 18, 27, 45, 50, 54, 60, 64, 84, 99, 132, 147, 153, 162, 207, 220, 225, 228, 240, 242, 243, 245, 255, 256, 264, 280, 297, 315, 325, 336, 338, 343, 348, 364, 369, 375, 423, 425, 435, 440, 455, 460, 468, 475, 477, 486, 487, 507, 539, 552

Offset: 1

Robert G. Wilson v, Jul 24 2015

nonn

Greater (member) of the n-th pair in A260310.
a(n) ~ 11.0*n.
It appears that most of the terms are composite (97.25% out of the first 10000 terms), but there are some primes: 487, 983, 1093, 1231, 1277, 2143, 2207, 2749, ..., .
a(n) < a(n+1) for all n > 0 is false, a(3276) = a(3277)= 35407 with A260409(3276) equal to 29820 & A260409(3276) equal to 34350 and a(4228) = a(4229) = 45841 with A260409(4228) equal to 40260 & A260409(4229) equal to 41496.
Least term a(n) such that a(n+1) is k away: 3276, 21, 2, 18, 6, 5, 7, 44, 1, 3, ..., . (A260410).
Conjecture: when a(n) is composite, A260408(n) is prime and vice versa. No contradictions in the first 10000 terms.

			see A260310.

Robert G. Wilson v, Table of n, a(n) for n = 1..9906

Cf. A260310, A260408, A260410.

(* first run the Mmca in A260310 and then *) Take[ Transpose[ lst][[2]], 60]

a(n) = A260310(2n).

A260410 Find smallest m such that A260409(m+1)-A260409(m) = n; then a(n) = A260409(m).

Original entry on oeis.org

3276, 21, 2, 18, 6, 5, 7, 44, 1, 3, 23, 30, 19, 16, 78, 10, 26, 27, 4, 183, 9, 57, 260, 58, 138, 84, 59, 80, 208, 281, 147, 476, 49, 11, 282, 192, 114, 290, 553, 222, 851, 1582, 1077, 293, 348, 15, 700, 155, 37, 1234, 1786, 93, 266, 1103

Offset: 0

Robert G. Wilson v, Jul 24 2015

nonn

a(71) = 8027, a(73) = 1316, a(74) = 7785, a(75) = 5407, a(80) = 9809, a(81) = 1739, a(97) = 8972 & a(98) = 9750.
In the first 9999 terms of the first differences of A260409, there are 2 zeros, 891 ones, 766 twos, etc.
These can be computed by first running the Mmca in A260310 and then Tally@ Sort @ Differences[ Transpose[ lst][[2]]]

			a(0) = 35407 because A260409(3276) = A260409(3277) = 35407 and the difference is 0.
a(8) = 8 because A260409(1) = 8 and A260409(2) = 16 and the difference is 8.
a(9) = 18 because A260409(3) = 18 and A260409(4) = 27, which has a difference of 9.

Cf. A260310, A260408, A260409.

(* first run the Mmca in A260310 and then *) t = Transpose[lst][[2]]; d = Differences[ Transpose[ lst][[2]]]; p = Table[ Position[d, n, 1, 1], {n, 0, 69}] // Flatten; t[[#]] & /@ p

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A260408 Bisection of A260310.

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A260409 Bisection of A260310.

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A260410 Find smallest m such that A260409(m+1)-A260409(m) = n; then a(n) = A260409(m).

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