A008348 -id:A008348 - cp's OEIS frontend

A324792 First differences of A325056: distance in A076042 from n-th low point to the next.

5, 5, 9, 15, 25, 45, 77, 133, 231, 401, 693, 1201, 2081, 3603, 6241, 10809, 18723, 32429, 56169, 97287, 168505, 291861, 505517, 875581, 1516551, 2626743, 4549653, 7880231, 13648959, 23640691, 40946879, 70922073, 122840635, 212766221, 368521905, 638298663

Offset: 0

N. J. A. Sloane, Sep 04 2019

Giovanni Resta, Table of n, a(n) for n = 0..41

Cf. A076042, A325056, A324791.

If we use primes instead of squares we get A008348, A309226, A324782, A324783.

a=b=c=d=n=0; L={0}; While[Length[L] < 22, n++; a=b; b=c; c=d; d=c + If[c < n^2, n^2, -n^2]; If[a > b < c < d, AppendTo[L, n-2]]]; Differences@ L (* Giovanni Resta, Oct 01 2019 *)

More terms from Giovanni Resta, Oct 01 2019

A325056 Index of n-th low point in A076042.

Original entry on oeis.org

0, 5, 10, 19, 34, 59, 104, 181, 314, 545, 946, 1639, 2840, 4921, 8524, 14765, 25574, 44297, 76726, 132895, 230182, 398687, 690548, 1196065, 2071646, 3588197, 6214940, 10764593, 18644824, 32293783, 55934474, 96881353, 167803426, 290644061, 503410282, 871932187

Offset: 0

N. J. A. Sloane, Sep 04 2019

nonn

N. J. A. Sloane, Table of n, a(n) for n = 0..3999 (Terms up through a(42) from Giovanni Resta.)
N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Cf. A076042, A324791, A324792.

If we use primes instead of squares we get A008348, A309226, A324782, A324783.

Maple
```
See A324791.
```

a=b=c=d=n=0; L={0}; While[Length[L] < 22, n++; a=b; b=c; c=d; d=c + If[c < n^2, n^2, -n^2]; If[a > b < c < d, AppendTo[L, n - 2]]]; L (* Giovanni Resta, Oct 01 2019 *)

PARI
```
\\ See PARI program in A076042.
```

a(14)-a(17) added by N. J. A. Sloane, Sep 30 2019
More terms from Giovanni Resta, Oct 01 2019
Modified definition to make offset 0. - N. J. A. Sloane, Oct 02 2019

A309222 a(0) = 6; thereafter a(n) = a(n-1) + prime(n) if prime(n) > a(n-1), otherwise a(n) = a(n-1) - prime(n).

Original entry on oeis.org

6, 4, 1, 6, 13, 2, 15, 32, 13, 36, 7, 38, 1, 42, 85, 38, 91, 32, 93, 26, 97, 24, 103, 20, 109, 12, 113, 10, 117, 8, 121, 248, 117, 254, 115, 264, 113, 270, 107, 274, 101, 280, 99, 290, 97, 294, 95, 306, 83, 310, 81, 314, 75, 316, 65, 322, 59, 328, 57, 334, 53, 336, 43, 350, 39, 352

Offset: 0

N. J. A. Sloane, Aug 29 2019

Hugo van der Sanden asks if this ever reaches 0. He finds that a(n) > 0 for n < 5*10^10. Probabilistic arguments suggest it will never reach 0.

Hugo van der Sanden, Posting to Sequence Fans Mailing List, Aug 28 2019

N. J. A. Sloane, Table of n, a(n) for n = 0..20000

If we start with 0 or 1 instead of 6 we get A008348, A022837.

Similar in spirit to A008344, and has a similar graph.

A330725 a(0) = 0; thereafter a(n) = a(n-1) + sigma(n) if sigma(n) > a(n-1), otherwise a(n) = a(n-1) - sigma(n), where sigma is the sum of divisors function A000203.

Original entry on oeis.org

0, 1, 4, 0, 7, 1, 13, 5, 20, 7, 25, 13, 41, 27, 3, 27, 58, 40, 1, 21, 63, 31, 67, 43, 103, 72, 30, 70, 14, 44, 116, 84, 21, 69, 15, 63, 154, 116, 56, 0, 90, 48, 144, 100, 16, 94, 22, 70, 194, 137, 44, 116, 18, 72, 192, 120, 0, 80, 170, 110, 278, 216, 120, 16

Offset: 0

Alois P. Heinz, Jan 11 2020

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Cf. A000203, A008344, A008345, A008348, A076042, A111466, A126646, A327442, A331165.

a:= proc(n) option remember; `if`(n=0, 0, ((s, t)-> s+
      `if`(s

nxt[{n_,a_}]:={n+1,If[DivisorSigma[1,n+1]>a,a+DivisorSigma[1,n+1],a- DivisorSigma[ 1,n+1]]}; NestList[nxt,{0,0},70][[All,2]] (* Harvey P. Dale, May 14 2022 *)

A331165 a(n) = a(n-1) + p(n) if p(n) > a(n-1), otherwise a(n) = a(n-1) - p(n), where p is the partition function A000041 (assuming a(n) = 0 for n < 0).

Original entry on oeis.org

1, 0, 2, 5, 0, 7, 18, 3, 25, 55, 13, 69, 146, 45, 180, 4, 235, 532, 147, 637, 10, 802, 1804, 549, 2124, 166, 2602, 5612, 1894, 6459, 855, 7697, 16046, 5903, 18213, 3330, 21307, 42944, 16929, 48114, 10776, 55359, 2185, 65446, 140621, 51487, 157045, 32291, 179564

Offset: 0

Alois P. Heinz, Jan 11 2020

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Cf. A000041, A008344, A008345, A008348, A076042, A111466, A126646, A327442, A330725.

a:= proc(n) option remember; `if`(n<0, 0, ((s, t)-> s+
     `if`(s

a[n_] := a[n] = If[n<0, 0, With[{a1 = a[n-1], p = PartitionsP[n]}, If[p>a1, a1 + p, a1 - p]]];
a /@ Range[0, 70] (* Jean-François Alcover, Jan 05 2021 *)

lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, my(p = numbpart(n-1)); va[n] = va[n-1] - p; if (va[n] < 0, va[n] += 2*p);); va;} \\ Michel Marcus, Jan 06 2021

A022836 a(n) = c(1)p(0) + ... + c(n)p(n-1), where c(i) = 1 if a(i-1) <= p(i-1) and c(i) = -1 if a(i-1) > p(i-1) (with p(0) = 1 and p(i) a prime for i >= 1).

Original entry on oeis.org

1, 3, 6, 1, 8, 19, 6, 23, 4, 27, 56, 25, 62, 21, 64, 17, 70, 11, 72, 5, 76, 3, 82, 165, 76, 173, 72, 175, 68, 177, 64, 191, 60, 197, 58, 207, 56, 213, 50, 217, 44, 223, 42, 233, 40, 237, 38, 249, 26, 253, 24, 257, 18, 259, 8, 265, 2, 271, 542, 265, 546, 263, 556

Offset: 0

Clark Kimberling

nonn

Alternate description: a(1) = 1, a(n) = a(n-1) - prime(n) if a(n-1) > prime(n) else a(n) = a(n-1) + prime(n). - Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 27 2003

Harvey P. Dale, Table of n, a(n) for n = 0..1000

nxt[{n_,a_}]:=Module[{p=Prime[n]},{n+1,If[a>p,a-p,a+p]}]; NestList[ nxt,{1,1},70][[All,2]] (* Harvey P. Dale, Nov 27 2016 *)

a(n) = A008348(n) + 1.

Name corrected by Sean A. Irvine, May 22 2019

cp's OEIS Frontend

A324792 First differences of A325056: distance in A076042 from n-th low point to the next.

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Extensions

A325056 Index of n-th low point in A076042.

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Author

Keywords

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Programs

Maple

Mathematica

PARI

Extensions

A309222 a(0) = 6; thereafter a(n) = a(n-1) + prime(n) if prime(n) > a(n-1), otherwise a(n) = a(n-1) - prime(n).

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A330725 a(0) = 0; thereafter a(n) = a(n-1) + sigma(n) if sigma(n) > a(n-1), otherwise a(n) = a(n-1) - sigma(n), where sigma is the sum of divisors function A000203.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A331165 a(n) = a(n-1) + p(n) if p(n) > a(n-1), otherwise a(n) = a(n-1) - p(n), where p is the partition function A000041 (assuming a(n) = 0 for n < 0).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A022836 a(n) = c(1)*p(0) + ... + c(n)*p(n-1), where c(i) = 1 if a(i-1) <= p(i-1) and c(i) = -1 if a(i-1) > p(i-1) (with p(0) = 1 and p(i) a prime for i >= 1).

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Author

Keywords

Comments

Links

Programs

Mathematica

Formula

Extensions

A022836 a(n) = c(1)p(0) + ... + c(n)p(n-1), where c(i) = 1 if a(i-1) <= p(i-1) and c(i) = -1 if a(i-1) > p(i-1) (with p(0) = 1 and p(i) a prime for i >= 1).