A246793 -id:A246793 - cp's OEIS frontend

A246795 a(n) = A246793(A005669(n)).

1, 1, 2, 3, 5, 5, 7, 8, 9, 8, 12, 10, 11, 12, 9, 12, 15, 10, 11, 15, 10, 17, 13, 16, 20, 17, 21, 19, 19, 24, 13, 23, 18, 21, 17, 26, 26, 29, 19, 23, 23, 25, 27, 27, 29, 24, 26, 25, 33, 28, 32, 32, 31, 36, 35, 37, 42, 33, 28, 35, 30, 36, 30, 34, 44, 29, 32, 34, 33, 30, 40, 38, 34, 44

Offset: 2

Farideh Firoozbakht, Oct 24 2014

This sequence evaluates the largest m's defined in A246793 for the index of primes where largest gaps occurs.
Conjecture: For every n, a(n) is positive.
a(75) = 44 and A246794(75) = 6 hence A182134(34952141021660495 - k) = k for 5 < k < 45, where 34952141021660495 = A005669(75).

Cf. A000040, A002386, A005669, A182134, A246785, A246794.

A252475 Indices of record values in A246793.

Original entry on oeis.org

2, 7, 15, 21, 30, 61, 90, 177, 216, 395, 965, 1628, 2206, 2212, 3040, 10727, 10954, 29529, 62758, 94357, 196992, 314967, 608805, 1258717, 1767289, 2449005, 7939395, 9373169, 16855002, 16855004, 32881951, 41084088, 83715358, 90288095, 151449068, 315082046

Offset: 1

Robert Price, Dec 17 2014

nonn

a(51) > 3.5*10^11.

Robert Price, Table of n, a(n) for n = 1..50

Cf. A000040, A182134, A246785, A252474, A246793.

A246785 a(n) is the least m>0 such that A182134(n - m) = m, or zero if there is no such m.

Original entry on oeis.org

1, 1, 1, 1, 0, 2, 2, 1, 0, 2, 2, 2, 0, 3, 2, 2, 0, 3, 0, 3, 0, 3, 2, 2, 0, 0, 4, 0, 2, 2, 2, 0, 3, 0, 4, 3, 0, 4, 4, 4, 3, 0, 4, 0, 4, 2, 2, 0, 0, 4, 0, 5, 4, 4, 3, 0, 0, 5, 0, 5, 3, 2, 0, 0, 4, 4, 2, 0, 0, 0, 5

Offset: 2

Farideh Firoozbakht, Oct 24 2014

nonn

Recall that A182134(k) is the number of primes p with prime(k) < p < prime(k)^(1+1/k). The record values up to n = 56000 are the positive integers up to 21 except 13 which first occurs after 14; A246790 gives indices of these record values.

Robert Price, Table of n, a(n) for n = 2..10000

Cf. A000040, A182134, A246790, A246793.

a246785 n = if null ms then 0 else head ms
            where ms = [m | m <- [1 .. n-1], a182134 (n - m) == m]
-- Reinhard Zumkeller, Nov 17 2014

h[n_]:= If[n==0, 0, (i=Prime[n]+1; j=Prime[n]^(1+1/n); Length[Select[Range[i,j], PrimeQ]])];a1[n_]:= (For[m=1, m<=n-1 && h[n-m]!= m, m++]; m); a[k_]:= If[c=a1[k]; c==k, 0, c]; Table[a[k],{k,2,90}]

cp's OEIS Frontend

A246795 a(n) = A246793(A005669(n)).

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A252475 Indices of record values in A246793.

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A246785 a(n) is the least m>0 such that A182134(n - m) = m, or zero if there is no such m.

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Haskell

Mathematica