A131741 -id:A131741 - cp's OEIS frontend

A236697 First differences of A131741.

1, 2, 6, 2, 16, 2, 6, 4, 26, 6, 10, 6, 12, 6, 20, 12, 18, 22, 14, 34, 6, 30, 8, 10, 26, 24, 6, 42, 10, 8, 4, 8, 22, 2, 34, 24, 8, 10, 54, 8, 42, 28, 6, 96, 26, 40, 14, 60, 4, 20, 30, 46, 26, 12, 42, 28, 2, 70, 8, 126, 4, 26, 34, 6, 42, 18, 96, 26, 48, 4

Offset: 1

Zak Seidov, Jan 30 2014

nonn

Among first 10000 terms, the largest is a(7790) = 17412.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A003002, A003003, A003278, A004793, A005047, A005487, A033157, A065825, A092482, A093678, A093679, A093680, A093681, A093682, A094870, A101884, A101886, A101888, A131741, A140577, A185256, A208746, A229037.

a(n) = A131741(n+1) - A131741(n).

A140577 Decimal expansion of Wroblewski's constant arising in nonaveraging sequences.

Original entry on oeis.org

3, 0, 0, 8, 4, 9

Offset: 1

Jonathan Vos Post, Jul 05 2008

A nonaveraging sequence contains no three terms which are in an arithmetic progression. Wroblewski (1984) showed that for infinite nonaveraging sequences Sup_{all nonaveraging sequences b(n)} Sum_{k>=1} 1/b(k) > 3.00849. [Typo corrected by Stefan Steinerberger, Aug 28 2008]

Steven R. Finch, "Erdos' Reciprocal Sum Constants." 2.20 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 163-166, 2003.
R. K. Guy, "Nonaveraging Sets. Nondividing Sets." C16 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 131-132, 1994.

Eric W. Weisstein, Nonaveraging Sequence.
J. Wroblewski, A Nonaveraging Set of Integers with a Large Sum of Reciprocals, Math. Comput. 43, 261-262, 1984.
Index entries related to non-averaging sequences

Cf. A051013, A131741, A133234.

A133234 a(n) is least semiprime (not already in list) such that no 3-term subset forms an arithmetic progression.

Original entry on oeis.org

4, 6, 9, 10, 15, 22, 25, 33, 39, 49, 55, 58, 82, 86, 87, 93, 111, 118, 121, 122, 134, 145, 185, 194, 201, 202, 206, 215, 237, 247, 274, 287, 298, 299, 303, 305, 314, 334, 335, 358, 362, 386, 446, 447, 454, 471, 482, 497, 502, 527, 529, 537, 553, 554, 562, 614

Offset: 1

Jonathan Vos Post, Oct 13 2007

This is to semiprimes A001358 as A131741 is to primes A000040.

Cf. A000040, A001358, A065825, A131741.

NextSemiprime[n_] := Block[{c = n + 1, f = 0}, While[Plus @@ Last /@ FactorInteger[c] != 2, c++ ]; c ]; f[l_List] := Block[{c, f = 0}, c = If[l == {}, 2, l[[ -1]]]; While[f == 0, c = NextSemiprime[c]; If[Intersection[l, l - (c - l)] == {}, f = 1]; ]; Append[l, c] ]; Nest[f, {}, 100] (* Ray Chandler, Nov 10 2007 *)

a(1) = 4, a(2) = 6, a(n) = smallest semiprime such that there is no i < j < n with a(n) - a(j) = a(j) - a(i).

More terms from Ray Chandler, Nov 10 2007

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A236697 First differences of A131741.

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A140577 Decimal expansion of Wroblewski's constant arising in nonaveraging sequences.

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A133234 a(n) is least semiprime (not already in list) such that no 3-term subset forms an arithmetic progression.

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