A141130 -id:A141130 - cp's OEIS frontend

A028815 a(n) = prime(n) + 1 (starting with 1).

2, 3, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 128, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284

Offset: 0

N. J. A. Sloane

n-th noncomposite (unit or prime) positive integer + 1.

The "0th prime" is defined to be 1 (a unit, formerly considered to be prime).

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A000040, A006093, A008578, A008864.

Cf. A141130, A141132, A141133, A141136, A141138.

A028815:= func< n | n eq 0 select 2 else 1 + NthPrime(n) >;
[A028815(n): n in [0..70]]; // G. C. Greubel, Aug 05 2024

Join[{2},Prime[Range[70]]+1] (* Harvey P. Dale, Oct 14 2019 *)

a(n) = if(n==0, 2, prime(n) + 1); \\ Altug Alkan, Mar 14 2018

def A028815(n): return 2 if n==0 else 1+nth_prime(n)
[A028815(n) for n in range(71)] # G. C. Greubel, Aug 05 2024

a(n) = prime(n) + 1 = A000040(n) + 1 = A008864(n) for n >= 1.
a(n) = A008578(n+1) + 1, n >= 0.
a(n) = 2*A006254(n-1), for n >= 2, with a(0) = 2, a(1) = 3. - G. C. Greubel, Aug 05 2024

A141132 a(n) = prime(prime(prime(prime(A028815(n) - 1) - 1) - 1) - 1) - 1.

Original entry on oeis.org

1, 2, 36, 576, 1492, 4512, 8110, 14778, 18222, 26416, 41452, 51576, 71740, 87552, 96352, 111372, 135660, 167106, 172152, 218550, 238990, 250252, 284148, 317856, 351706, 400408, 441478, 463398, 490246, 505780, 527280, 643990, 679036, 718182

Offset: 0

Juri-Stepan Gerasimov, Jul 31 2008

nonn

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A000040, A028815, A141130, A141133, A141136, A141138.

p:=NthPrime;
A141132:= func< n | n eq 0 select 1 else p(p(p(p(p(n))-1)-1)-1)-1 >;
[A141132(n): n in [0..50]]; // G. C. Greubel, Aug 05 2024

A141132[n_]:= With[{p=Prime}, If[n==0, 1, p[p[p[p[p[n]]-1]-1]-1]-1 ]];
Table[A141132[n], {n, 0, 60}] (* G. C. Greubel, Aug 05 2024 *)

p=nth_prime
def A141132(n): return 1 if n==0 else p(p(p(p(p(n))-1)-1)-1)-1
[A141132(n) for n in range(51)] # G. C. Greubel, Aug 05 2024

a(n) = prime(prime(prime(prime(prime(n)) - 1) - 1) - 1) - 1, with a(0) = 1. - G. C. Greubel, Aug 05 2024

Extended by D. S. McNeil, Mar 21 2009

Offset changed by G. C. Greubel, Aug 05 2024

A141133 a(n) = prime(prime(prime(A028815(n) - 1) - 1) - 1) - 1.

Original entry on oeis.org

1, 2, 12, 106, 238, 612, 1020, 1732, 2088, 2902, 4336, 5278, 7102, 8500, 9282, 10566, 12640, 15268, 15678, 19488, 21142, 22062, 24766, 27430, 30108, 33892, 37056, 38706, 40786, 41980, 43626, 52360, 54982, 57900, 60496, 66808, 68398, 72670

Offset: 0

Juri-Stepan Gerasimov, Jul 31 2008

nonn

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A000040, A028815, A141130, A141132, A141136, A141138.

p:=NthPrime;
A141133:= func< n | n eq 0 select 1 else p(p(p(p(n))-1)-1) -1 >;
[A141133(n): n in [0..50]]; // G. C. Greubel, Aug 05 2024

A141133[n_]:= With[{p=Prime}, If[n==0, 1, p[p[p[p[n]]-1]-1]-1 ]];
Table[A141133[n], {n,0,60}] (* G. C. Greubel, Aug 05 2024 *)

p=nth_prime
def A141133(n): return 1 if n==0 else p(p(p(p(n))-1)-1)-1
[A141133(n) for n in range(51)] # G. C. Greubel, Aug 05 2024

a(n) = prime(prime(prime(prime(n)) - 1) - 1) - 1, with a(0) = 1. - G. C. Greubel, Aug 05 2024

Corrected and extended by D. S. McNeil, Mar 21 2009

Offset changed by G. C. Greubel, Aug 05 2024

A141136 a(n) = prime(prime(A028815(n) - 1) - 1) - 1.

Original entry on oeis.org

1, 2, 6, 28, 52, 112, 172, 270, 316, 420, 592, 700, 910, 1060, 1150, 1290, 1510, 1782, 1830, 2212, 2376, 2472, 2740, 2998, 3256, 3630, 3930, 4078, 4270, 4390, 4546, 5350, 5590, 5866, 6100, 6658, 6802, 7186, 7602, 7828, 8218, 8520, 8712, 9310, 9438, 9732

Offset: 0

Juri-Stepan Gerasimov, Jul 31 2008

nonn

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A000040, A028815, A141130, A141132, A141133, A141138.

p:=NthPrime;
A141136:= func< n | n eq 0 select 1 else p(p(p(n))-1) -1 >;
[A141136(n): n in [0..50]]; // G. C. Greubel, Aug 05 2024

A141136[n_]:= With[{p=Prime}, If[n==0, 1, p[p[p[n]]-1]-1]];
Table[A141136[n], {n,0,60}] (* G. C. Greubel, Aug 05 2024 *)

p=nth_prime
def A141136(n): return 1 if n==0 else p(p(p(n))-1)-1
[A141136(n) for n in range(51)] # G. C. Greubel, Aug 05 2024

a(n) = A000040(A000040(A000040(n)) - 1) - 1, with a(0) = 1. - G. C. Greubel, Aug 05 2024

Corrected and extended by D. S. McNeil, Mar 21 2009

Offset changed by G. C. Greubel, Aug 05 2024

A141138 a(n) = prime(A028815(n) - 1) - 1.

Original entry on oeis.org

1, 2, 4, 10, 16, 30, 40, 58, 66, 82, 108, 126, 156, 178, 190, 210, 240, 276, 282, 330, 352, 366, 400, 430, 460, 508, 546, 562, 586, 598, 616, 708, 738, 772, 796, 858, 876, 918, 966, 990, 1030, 1062, 1086, 1152, 1170, 1200, 1216, 1296, 1408, 1432, 1446, 1470

Offset: 0

Juri-Stepan Gerasimov, Jul 31 2008

nonn

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A028815, A141130, A141132, A141133, A141136.

A141138:= func< n | n eq 0 select 1 else NthPrime(NthPrime(n)) -1 >;
[A141138(n): n in [0..50]]; // G. C. Greubel, Aug 05 2024

A141138[n_]:= If[n==0, 1, Prime[Prime[n]] -1];
Table[A141138[n], {n,0,70}] (* G. C. Greubel, Aug 05 2024 *)

def A141138(n): return 1 if n==0 else nth_prime(nth_prime(n))-1
[A141138(n) for n in range(71)] # G. C. Greubel, Aug 05 2024

a(n) = A000040(A000040(n)) - 1, with a(0) = 1. - G. C. Greubel, Aug 05 2024

a(14), a(28) corrected by D. S. McNeil, Mar 21 2009

Offset changed by G. C. Greubel, Aug 05 2024

A373016 a(n) is the least positive integer k such that 3n^2 + 2n + k is a square.

Original entry on oeis.org

4, 9, 3, 8, 15, 1, 8, 17, 28, 4, 15, 28, 43, 9, 24, 41, 60, 16, 35, 56, 4, 25, 48, 73, 11, 36, 63, 92, 20, 49, 80, 113, 31, 64, 99, 9, 44, 81, 120, 20, 59, 100, 143, 33, 76, 121, 3, 48, 95, 144, 16, 65, 116, 169, 31, 84, 139, 196, 48, 105, 164, 8, 67, 128, 191, 25, 88, 153, 220, 44, 111, 180

Offset: 1

Claude H. R. Dequatre, May 20 2024

The scatterplot shows an interesting crosshatch structure where all terms are at the intersection of ascending and descending hatches.
Terms on each hatch are quite well fitted by a polynomial of degree 2.
For terms on ascending hatches, the parity of the term indices does not change on a given hatch but alternates from one hatch to the next and on the same hatch, the parity of two consecutive terms alternates.
For terms on descending hatches, the parity of the indices of two consecutive terms alternates on the same hatch and that of terms does not change on the same hatch but alternates from one hatch to the next.
All squares exclusively are in ascending order on the same ascending hatch at n = 6, 10, 14, 18, 22, ... but some squares can be also found at the intersection of other hatches.
The first differences of the indices of the terms located on ascending and descending hatches are respectively equal to 4 and 3. For terms that are on the ascending and descending hatches, the differences of order 2 quickly become constant and equal to 2 and 4, respectively.
The fixed points begin 3, 48, 675, 9408, etc. They are all divisible by 3 and their parity seems to alternate. It appears that they are the positive terms of A007654.

			a(1) = 4 because 3*1^2 + 2*1 = 5 and 5 + 1, 5 + 2, 5 + 3 are not squares, but 5 + 4 is. So, 4 is a term.
a(2) = 9 because 3*2^2 + 2*2 = 16 and 16 + 1, 16 + 2, 16 + 3, 16 + 4, 16 + 5, 16 + 6, 16 + 7, 16 + 8 are not squares, but 16 + 9 is. So, 9 is a term.

Cf. A000005, A000290, A005408.
Cf. A045944, A080883.
Cf. A373026, A373028.
Sequences with similar scatterplot and pin plot graphs: A141130, A141131, A141134, A141135.

a(n)=my(t=3*n^2+2*n); (sqrtint(t)+1)^2-t \\ Charles R Greathouse IV, May 21 2024

a(n) is the smallest square greater than 3*n^2 + 2*n, minus 3*n^2 + 2*n. - Charles R Greathouse IV, May 21 2024
1 <= a(n) <= floor(sqrt(12)*n) + 3. I believe both bounds are tight infinitely often. - Charles R Greathouse IV, May 21 2024
a(n) = A080883(A045944(n)). - Michel Marcus, May 22 2024

cp's OEIS Frontend

A028815 a(n) = prime(n) + 1 (starting with 1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

SageMath

Formula

A141132 a(n) = prime(prime(prime(prime(A028815(n) - 1) - 1) - 1) - 1) - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

Extensions

A141133 a(n) = prime(prime(prime(A028815(n) - 1) - 1) - 1) - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

Extensions

A141136 a(n) = prime(prime(A028815(n) - 1) - 1) - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

Extensions

A141138 a(n) = prime(A028815(n) - 1) - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

Extensions

A373016 a(n) is the least positive integer k such that 3*n^2 + 2*n + k is a square.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Formula

A373016 a(n) is the least positive integer k such that 3n^2 + 2n + k is a square.