A246790 -id:A246790 - cp's OEIS frontend

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

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}]

A246793 a(n) is the largest m such that A182134(n - k) = k for A246785(n) <= k <= m, or zero if there is no such m.

Original entry on oeis.org

1, 1, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 3, 3, 2, 0, 3, 0, 4, 0, 4, 3, 2, 0, 0, 4, 0, 5, 2, 2, 0, 3, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 0, 5, 4, 2, 0, 0, 4, 0, 5, 5, 4, 4, 0, 0, 5, 0, 6, 5, 3, 0, 0, 4, 4, 4, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 0, 5, 0, 6, 0, 0, 7

Offset: 1

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). Obviously a(n) = 0 if and only if A246785(n) = 0.

			A182134(217 - k) = k for k = 3, 4, ..., 9 since A246785(217) = 3 and a(217) = 9.

Robert Price, Table of n, a(n) for n = 1..10000

Cf. A000040, A182134, A246785, A246790.

np[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&& np[n-m] != m, m++];m);a2[k_]:= If[c=a1[k]; c==k,0,c]; a[n_]:= If[a2[n]==0, 0, For[r=a2[n], np[n-r]==r, r++]; r-1]; Table[a[k], {k,2,90}]

A252474 Record values in A246785.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 59, 60, 61

Offset: 1

Robert Price, Dec 17 2014

For all known terms of this sequence, a(n+1) < a(n)+3; is this true for all terms? - Farideh Firoozbakht, Dec 20 2014
Integers not in this sequence begin: 13, 31, 34, 51, 54, 56, 58.
The comment above could also be phrased as "no two consecutive numbers in the complement" or "no gaps larger than one". But one sees that the missing numbers become more frequent towards larger values, so the answer to the question might well be "no". - Robert Price, Jan 06 2015

Cf. A182134, A246785, A246790.

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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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A246793 a(n) is the largest m such that A182134(n - k) = k for A246785(n) <= k <= m, or zero if there is no such m.

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A252474 Record values in A246785.

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