A127485 -id:A127485 - cp's OEIS frontend

A127483 Numbers n such that A100705(n) = n^3 + (n+1)^2 is prime.

1, 2, 3, 4, 8, 9, 13, 14, 15, 17, 22, 23, 24, 25, 30, 32, 34, 35, 38, 39, 42, 45, 50, 58, 60, 64, 65, 79, 83, 85, 88, 90, 92, 94, 98, 99, 100, 102, 113, 115, 122, 125, 127, 130, 133, 134, 137, 140, 144, 147, 148, 153, 154, 157, 164, 167, 170, 178, 179, 184, 190, 193

Offset: 1

Alexander Adamchuk, Jan 16 2007

nonn

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 a(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 start with n = {1,2,3,8,13,14,22,23,24,34,38,64,98,99,,...} = A127484, or numbers n such that a(n) = a(n+1) - 1.
Triplets start with n = {1,2,13,22,23,98,253,343,573,638,702,...} = A127485, or numbers n such that a(n) = a(n+1) - 1 = a(n+2) - 2.
Quadruplets start with n = {1,22,13077,14267,16092,16267,162,...} = A127486.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A100705, A100662, A127484, A127485, A127486.

Select[Range[1000],PrimeQ[ #^3+(#+1)^2]&]

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

Original entry on oeis.org

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]&]

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

cp's OEIS Frontend

A127483 Numbers n such that A100705(n) = n^3 + (n+1)^2 is prime.

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

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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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