A118939 -id:A118939 - cp's OEIS frontend

A118940 Primes p such that (p^2+7)/8 is prime.

3, 7, 17, 23, 41, 47, 71, 89, 103, 113, 127, 137, 151, 191, 193, 199, 223, 263, 271, 281, 337, 359, 401, 439, 457, 503, 521, 569, 577, 599, 641, 719, 727, 751, 839, 857, 863, 881, 887, 929, 991, 1009, 1033, 1097, 1103, 1151, 1193, 1217, 1231, 1279, 1297, 1303

Offset: 1

T. D. Noe, May 06 2006

nonn

For all primes q>2, we have q=4k+-1 for some k, which makes it easy to show that 8 divides q^2+7.

Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118939, A118941 and A118942.

Select[Prime[Range[200]],PrimeQ[(#^2+7)/8]&]

lista(nn) = {forprime(p=2, nn, iferr(if (isprime(q=(p^2+7)/8), print1(q, ", ")), E, ););} \\ Michel Marcus, Feb 18 2018

A118941 Primes p such that (p^2-5)/4 is prime.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 23, 31, 41, 43, 53, 61, 71, 79, 83, 89, 97, 101, 107, 109, 113, 131, 137, 167, 173, 179, 193, 229, 241, 251, 263, 269, 277, 281, 283, 307, 311, 317, 349, 353, 373, 383, 419, 431, 439, 461, 463, 467, 563, 571, 577, 593, 607, 613, 619, 647

Offset: 1

T. D. Noe, May 06 2006

nonn

For all primes q>2, we have q=4k+-1 for some k, which makes it easy to show that 4 divides q^2-5. Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118939, A118940 and A118942.

Select[Prime[Range[200]],PrimeQ[(#^2-5)/4]&]

A118942 Primes p such that (p^2-13)/12 is prime.

Original entry on oeis.org

7, 13, 17, 19, 23, 31, 37, 41, 53, 67, 71, 73, 89, 103, 107, 113, 131, 139, 157, 163, 181, 199, 211, 233, 239, 257, 269, 283, 307, 311, 337, 359, 373, 379, 401, 419, 463, 487, 491, 499, 509, 521, 577, 593, 607, 617, 631, 647, 653, 683, 701, 733, 761, 769, 787

Offset: 1

T. D. Noe, May 06 2006

nonn

For all primes q>3, we have q=6k+-1 for some k, which makes it easy to show that 12 divides q^2-13. Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118939, A118940 and A118941.

Select[Prime[Range[200]],PrimeQ[(#^2-13)/12]&]

A180082 Semiprime centered cube numbers: m^3 + (m+1)^3.

Original entry on oeis.org

9, 35, 91, 341, 559, 1241, 6119, 7471, 17261, 19909, 75241, 143009, 257651, 323839, 671509, 860851, 967591, 1433969, 1482571, 1970299, 2348641, 2772559, 3413159, 4548059, 5313691, 5666509, 7233841, 7520291, 9568441

Offset: 1

Jonathan Vos Post, Feb 06 2011

There are no prime centered cube numbers because m^3 + (m+1)^3 = (2m+1)*(m^2+m+1). - Zak Seidov, Feb 08 2011
Products of two primes p and q = (p^2+3)/4 with p's in A118939. - Zak Seidov, Feb 08 2011
From Lamine Ngom, Apr 17 2021: (Start)
Also numbers which are products of two primes whose sum and difference are both promic (A002378).
Subsequence of A217843 (sums of consecutive nonnegative cubes) limited to the terms that have only two prime factors (multiplicity counted).
As stated in A217843, any number that is the sum of consecutive nonnegative cubes can also be expressed as the product of two integers whose sum and difference are both promic. (Therefore, it cannot be prime.) It can also be expressed as the difference of the squares of two triangular numbers (A000217); thus, the two primes that are the factors of any term of this sequence are respectively the sum and difference of two triangular numbers. (End)

			a(1) = 1^3 + (1+1)^3 = 9 = 3^2 is semiprime.
a(2) = 2^3 + (2+1)^3 = 35 = 5 * 7.
a(3) = 3^3 + (3+1)^3 = 91 = 7 * 13.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001222, A001358, A005898.

Cf. A217843, A000217, A002378.

Select[Total/@Partition[Range[200]^3,2,1],PrimeOmega[#]==2&] (* Harvey P. Dale, Feb 02 2019 *)

A001358 INTERSECTION A005898.

More terms from Vincenzo Librandi, Feb 06 2011

cp's OEIS Frontend

A118940 Primes p such that (p^2+7)/8 is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

A118941 Primes p such that (p^2-5)/4 is prime.

Views

Author

Keywords

Comments

Programs

Mathematica

A118942 Primes p such that (p^2-13)/12 is prime.

Views

Author

Keywords

Comments

Programs

Mathematica

A180082 Semiprime centered cube numbers: m^3 + (m+1)^3.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions