A127483 -id:A127483 - cp's OEIS frontend

A127484 Numbers k such that A127483(k) = A127483(k+1) - 1.

1, 2, 3, 8, 13, 14, 22, 23, 24, 34, 38, 64, 98, 99, 133, 147, 153, 178, 232, 253, 254, 297, 328, 343, 344, 367, 407, 498, 573, 574, 582, 587, 624, 638, 639, 653, 668, 679, 702, 703, 759, 772, 793, 797, 849, 874, 944, 958, 1023, 1058, 1067, 1087, 1203, 1212, 1322

Offset: 1

Alexander Adamchuk, Jan 16 2007

nonn

A127483(n) = {1,2,3,4,8,9,13,14,15,17,22,23,24,25,30,32,34,35,38,39,42,45,50,...} are the numbers n such that A100705(n) = n^3 + (n+1)^2 is prime.
Corresponding primes of the form n^3 + (n+1)^2 are listed in A100662(n) = {5, 17, 43, 89, 593, 829, 2393, 2969, 3631, 5237, ...}.
Note that there are many consecutive twins, triples and quadruplets in A127483(n). For example: (1,2,3,4), {8,9}, {13,14,15}, {22,23,24,25}, {34,35}, {38,39}, {64,65}, {98,99,100}. Twins in A127483(k) start with numbers k = a(n). Triplets in A127483(k) start with k = {1,2,13,22,23,98,253,343,573,638,702,...} = A127485, or numbers n such that a(k) = a(k+1) - 1 = a(k+2) - 2. Quadruplets in A127483(k) start with k = {1,22,13077,14267,16092,16267,16282,36387,47012,51912,54662,...} = A127486.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A100705, A100662, A127483, A127485, A127486.

[k:k in [1..1350]|IsPrime(k^3+(k+1)^2) and IsPrime((k+1)^3+(k+2)^2)]; // Marius A. Burtea, Jan 20 2020

Select[Range[3000],PrimeQ[ #^3+(#+1)^2]&&PrimeQ[(#+1)^3+(#+2)^2]&]

A127485 Numbers k such that A127483(k) = A127483(k+1) - 1 = A127483(k+2) - 2.

Original entry on oeis.org

1, 2, 13, 22, 23, 98, 253, 343, 573, 638, 702, 1322, 1862, 2543, 2638, 2758, 2792, 2912, 3093, 3158, 3242, 3578, 3968, 4382, 5013, 6503, 7048, 7877, 8372, 8912, 9022, 9207, 10298, 10443, 11538, 12482, 13077, 13078, 13868, 14267, 14268, 14323, 14783

Offset: 1

Alexander Adamchuk, Jan 16 2007

nonn

A127483(n) = {1,2,3,4,8,9,13,14,15,17,22,23,24,25,30,32,34,35,38,39,42,45,50,...} are the numbers n such that A100705(n) = n^3 + (n+1)^2 is prime. Corresponding primes of the form n^3 + (n+1)^2 are listed in A100662(n) = {5, 17, 43, 89, 593, 829, 2393, 2969, 3631, 5237, ...}. Note that there are many consecutive twins, triples and quadruplets in A127483(n). For example: (1,2,3,4), {8,9}, {13,14,15}, {22,23,24,25}, {34,35}, {38,39}, {64,65}, {98,99,100}. Twins in A127483(k) start with k = {1,2,3,8,13,14,22,23,24,34,38,64,98,99,133,147,153,178,232,253,254,297,328,343, 344,367,407,498,...} = A127484. Triplets in A127483(k) start with numbers k = a(n). Quadruplets in A127483(k) start with k = {1,22,13077,14267,16092,16267,16282,36387,47012,51912,54662,...} = A127486.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A100705, A100662, A127483, A127484, A127486.

f:=func; [k:k in [1..15000]|f(k) and f(k+1) and f(k+2)]; // Marius A. Burtea, Jan 20 2020

Select[Range[30000],PrimeQ[ #^3+(#+1)^2]&&PrimeQ[(#+1)^3+(#+2)^2]&&PrimeQ[(#+2)^3+(#+3)^2]&]

A127486 Numbers k such that A127483(k) = A127483(k+1) - 1 = A127483(k+2) - 2 = A127483(k+3) - 3.

Original entry on oeis.org

1, 22, 13077, 14267, 16092, 16267, 16282, 36387, 47012, 51912, 54662, 144487, 181777, 205897, 210022, 213982, 250517, 263717, 344092, 409697, 454607, 568777, 643677, 665917, 702947, 749967, 824167, 858187, 887677, 888427, 997787, 1075537

Offset: 1

Alexander Adamchuk, Jan 16 2007

A127483(n) = {1,2,3,4,8,9,13,14,15,17,22,23,24,25,30,32,34,35,38,39,42,45,50,...} are the numbers n such that A100705(n) = n^3 + (n+1)^2 is prime. Corresponding primes of the form n^3 + (n+1)^2 are listed in A100662(n) = {5, 17, 43, 89, 593, 829, 2393, 2969, 3631, 5237, ...}. Note that there are many consecutive twins, triples and quadruplets in A127483(n). For example: (1,2,3,4), {8,9}, {13,14,15}, {22,23,24,25}, {34,35}, {38,39}, {64,65}, {98,99,100}. Twins in A127483(k) start with k = {1,2,3,8,13,14,22,23,24,34,38,64,98,99,133,147,153,178,232,253,254,297,328,343, 344,367,407,498,...} = A127484. Triplets in A127483(k) start with k = {1,2,13,22,23,98,253,343,573,638,702,...} = A127485. Quadruplets in A127483(k) start with numbers k = a(n).

For n>1 the final digit of all listed terms of a(n) is 2 or 7. - Alexander Adamchuk, Jan 16 2007

Amiram Eldar, Table of n, a(n) for n = 1..3000

Cf. A100705, A100662, A127483, A127484, A127485.

f[s_]:=s^3+(s+1)^2; Do[If[PrimeQ[f[n]]&&PrimeQ[f[n+1]]&&PrimeQ[f[n+2]]&&PrimeQ[f[n+3]],Print[n]],{n,1,100000}]

More terms from Alexander Adamchuk, Jan 16 2007

A100662 Primes of the form k^3 + (k+1)^2.

Original entry on oeis.org

5, 17, 43, 89, 593, 829, 2393, 2969, 3631, 5237, 11177, 12743, 14449, 16301, 27961, 33857, 40529, 44171, 56393, 60919, 75937, 93241, 127601, 198593, 219721, 266369, 278981, 499439, 578843, 621521, 689393, 737281, 787337, 839609, 950993, 980299, 1010201, 1071817

Offset: 1

Giovanni Teofilatto, Jan 03 2005

			a(1) = 5 because 5 = 1^3 + 2^2.
a(2) = 17 because 17 = 2^3 + 3^2.
a(3) = 43 because 43 = 3^3 + 4^2.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Intersection of A100705 and A000040.

Cf. A127483.

[ a: n in [0..100] | IsPrime(a) where a is n^3 + (n+1)^2 ]; // Vincenzo Librandi, Jul 18 2012

Select[Table[n^3+(n+1)^2,{n,200}],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)

list(lim)=my(v=List(),t); for(n=1,lim, t=n^3+(n+1)^2; if(t>lim, break); if(isprime(t), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Dec 23 2016

a(n) = A100705(A127483(n)). - Elmo R. Oliveira, Apr 19 2025

More terms from Mark Hudson, Jan 04 2005

cp's OEIS Frontend

A127484 Numbers k such that A127483(k) = A127483(k+1) - 1.

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A127485 Numbers k such that A127483(k) = A127483(k+1) - 1 = A127483(k+2) - 2.

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A127486 Numbers k such that A127483(k) = A127483(k+1) - 1 = A127483(k+2) - 2 = A127483(k+3) - 3.

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A100662 Primes of the form k^3 + (k+1)^2.

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