A228592 -id:A228592 - cp's OEIS frontend

A186945 The smallest integer x > 0 such that the number of terms of A050376 in (x/2,x] equals n.

2, 3, 5, 13, 17, 25, 31, 49, 61, 71, 73, 81, 103, 109, 113, 131, 139, 157, 173, 181, 191, 193, 199, 239, 241, 257, 269, 271, 283, 289, 293, 313, 353, 361, 373, 379, 409, 419, 421, 433, 439, 443, 463, 491, 499, 509, 571, 577, 599, 601, 607, 613, 619, 643, 647

Offset: 1

Vladimir Shevelev, Aug 30 2013

nonn

The sequence is an analog of Labos primes (A080359) in Fermi-Dirac arithmetic, since in this arithmetic terms of A050376 play role of primes (see comments in A050376).

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Cf. A080359, A228520, A228592.

a(n) <= A228520(n).

More terms from Peter J. C. Moses

A186946 The smallest integer x > 0 such that the number of prime powers p^k (k>=1) in (x/2,x] equals n.

Original entry on oeis.org

2, 3, 5, 9, 13, 25, 29, 31, 43, 49, 71, 73, 81, 103, 109, 113, 127, 131, 139, 157, 173, 181, 191, 193, 199, 239, 241, 269, 271, 283, 289, 293, 313, 349, 353, 361, 373, 379, 409, 419, 421, 433, 439, 443, 463, 499, 509, 523, 571, 577, 599, 601, 607, 613, 619

Offset: 1

Vladimir Shevelev, Aug 30 2013

nonn

An analog of Labos primes (A080359) on prime powers > 1 (A000961).

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Cf. A080459, A186945, A228520, A228592.

a000961Q[n_]:=(Length[FactorInteger[n]]==1) && IntegerQ[n]; nn=99; t=Table[0,{nn+1}]; s=0; Do[If[a000961Q[k], s++]; If[a000961Q[k/2], s--]; If[s<=nn && t[[s+1]]==0, t[[s+1]]=k], {k, 2, Prime[3*nn]}]; Prepend[Rest[t],2] (* after T. D. Noe's code at A080359 *) (* Peter J. C. Moses, Sep 11 2013 *)

a(n) <= A186945(n).

More terms from Peter J. C. Moses, Aug 30 2013

A188672 a(n) is the least r > 1 for which the interval (rn, r(n+1)) contains no prime powers (p^k, k >= 1), or a(n) = 0 if no such r exists.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 3, 0, 0, 0, 6, 2, 2, 3, 2, 7, 4, 2, 4, 0, 2, 7, 2, 2, 4, 3, 2, 2, 4, 2, 4, 4, 2, 2, 3, 5, 5, 2, 2, 3, 2, 2, 2, 3, 2, 4, 3, 2, 3, 4, 2, 0, 2, 2, 2, 5, 2, 3, 4, 2, 5, 2, 2, 3, 3, 2, 2, 2, 2, 4, 4, 2, 2, 3, 2, 2, 3, 2, 4, 3, 2, 3, 2

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, Aug 26 2013

nonn

Conjecture: a(n) = 0, iff n = 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 24, 56.

A proof that the interval(r*n, r*(n+1)) for r > 1 always contains a term from A000961 for n = 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 24, 56 uses methods based on the corresponding analog of Ramanujan numbers (cf. A228592) and their generalization.

Cf. A000961, A218831, A228518, A228592.

If a(n)*A228518(n) is not 0, then a(n) >= A228518(n).

cp's OEIS Frontend

A186945 The smallest integer x > 0 such that the number of terms of A050376 in (x/2,x] equals n.

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A186946 The smallest integer x > 0 such that the number of prime powers p^k (k>=1) in (x/2,x] equals n.

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A188672 a(n) is the least r > 1 for which the interval (rn, r(n+1)) contains no prime powers (p^k, k >= 1), or a(n) = 0 if no such r exists.

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cp's OEIS Frontend

A186945 The smallest integer x > 0 such that the number of terms of A050376 in (x/2,x] equals n.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A186946 The smallest integer x > 0 such that the number of prime powers p^k (k>=1) in (x/2,x] equals n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A188672 a(n) is the least r > 1 for which the interval (r*n, r*(n+1)) contains no prime powers (p^k, k >= 1), or a(n) = 0 if no such r exists.

Views

Author

Keywords

Comments

Crossrefs

Formula

A188672 a(n) is the least r > 1 for which the interval (rn, r(n+1)) contains no prime powers (p^k, k >= 1), or a(n) = 0 if no such r exists.