A246785 -id:A246785 - cp's OEIS frontend

A246790 Indices of record values in A246785.

2, 7, 15, 28, 53, 90, 177, 213, 216, 393, 395, 1628, 2206, 2212, 7075, 10364, 10727, 10954, 43444, 46099, 62758, 94347, 196989, 214629, 214631, 608803, 889740, 1353804, 2010048, 2449005, 7939395, 9373169, 16855002, 16855008, 41084086, 80005684, 113726074

Offset: 1

Farideh Firoozbakht, Oct 24 2014

nonn

The record values up to n = 56000: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21. Note that 13 is not a record value.
See A252474 for additional record values.
a(55) > 3.5*10^11. - Robert Price, Dec 17 2014

			a(13) = 2206 and A246785(2206) = 14. Note that 13 is not a record value.

Robert Price, Table of n, a(n) for n = 1..54

Cf. A000040, A182134, A246785, A252474.

a(21)-a(54) from Robert Price, Dec 17 2014

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}]

A246794 a(n) = A246785(A005669(n)).

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 4, 3, 5, 7, 5, 5, 4, 4, 3, 4, 4, 4, 5, 5, 5, 4, 7, 11, 8, 7, 8, 5, 10, 3, 4, 6, 9, 6, 8, 12, 8, 4, 10, 6, 9, 10, 7, 9, 4, 6, 7, 10, 7, 8, 5, 8, 10, 9, 8, 8, 4, 6, 7, 8, 9, 2, 10, 7, 6, 9, 8, 6, 4, 4, 7, 4, 6

Offset: 2

Farideh Firoozbakht, Oct 25 2014

Conjecture: For every n, a(n) is positive.

a(64) = 2 and A246795(64) = 30 hence A182134(49749629143526 - k) = k for 1 < k < 31, where 49749629143526 = A005669(64).

Cf. A000040, A002386, A005669, A182134, A246785, A246795.

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.

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

Original entry on oeis.org

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.

cp's OEIS Frontend

A246790 Indices of record values in A246785.

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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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A246794 a(n) = A246785(A005669(n)).

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A252474 Record values in A246785.

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

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A252475 Indices of record values in A246793.

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