A090161 -id:A090161

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A023219

Primes p such that 5p+6 is a prime.

+10
10

5, 7, 11, 13, 19, 29, 37, 41, 47, 53, 61, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 149, 151, 163, 181, 193, 197, 211, 229, 233, 239, 257, 263, 271, 293, 313, 347, 359, 373, 379, 389, 401, 421, 431, 443, 449, 461, 467, 487, 503, 509, 523, 541, 547, 557, 569, 571, 593

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988

Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

LINKS

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

J. Chavoya, A. Lucero, S. Reynolds, On p-adic valuations of the generalized Fibonacci sequences, in MSRI-UP Research Reports, 2014, pp. 91-109.

MATHEMATICA

Select[Prime[Range[200]], PrimeQ[5#+6]&] (* Harvey P. Dale, Jul 27 2011 *)

PROG

(Magma) [p: p in PrimesUpTo(200)| IsPrime(5*p+6)]; // Vincenzo Librandi, Nov 20 2010

CROSSREFS

Subset of A081759.

Cf. A090161, A088555, A088561.

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

A088555

Primes of the form 5*p + 6 where p is a prime.

+10
4

31, 41, 61, 71, 101, 151, 191, 211, 241, 271, 311, 401, 421, 491, 521, 541, 571, 641, 661, 691, 701, 751, 761, 821, 911, 971, 991, 1061, 1151, 1171, 1201, 1291, 1321, 1361, 1471, 1571, 1741, 1801, 1871, 1901, 1951, 2011, 2111, 2161, 2221, 2251, 2311, 2341

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes arising in A023219.

Subsequence of A030430.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..3400

FORMULA

a(n) = 5*A023219(n) + 6.

MATHEMATICA

6 + 5 Select[Prime[Range[200]], PrimeQ[5 # + 6] &] (* Vincenzo Librandi, May 19 2017 *)

PROG

(Magma) [5*p+6: p in PrimesUpTo(600)| IsPrime(5*p+6)]; // Vincenzo Librandi, May 19 2017

(PARI) forprime(p=2, 500, my(pp=5*p+6); if(isprime(pp), print1(pp, ", "))) \\ Hugo Pfoertner, Aug 06 2021

CROSSREFS

Cf. A023219, A030430, A088561, A090161.

KEYWORD

nonn,easy

AUTHOR

Ray Chandler, Nov 28 2003

EXTENSIONS

Name clarified by Jinyuan Wang, Aug 06 2021

STATUS

approved

A088561

A088555 indexed by A000040.

+10
3

11, 13, 18, 20, 26, 36, 43, 47, 53, 58, 64, 79, 82, 94, 98, 100, 105, 116, 121, 125, 126, 133, 135, 142, 156, 164, 167, 178, 190, 193, 197, 210, 216, 218, 233, 248, 271, 279, 286, 291, 297, 305, 318, 326, 331, 335, 344, 347, 362, 369, 374, 381, 395, 400, 406

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Subset of A049511.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(n) = k such that A000040(k) = A088555(n).

a(n) = A000720(A088555(n)). - Michel Marcus, Aug 06 2021

CROSSREFS

Cf. A023219, A049511, A088555, A090161.

KEYWORD

nonn,easy

AUTHOR

Ray Chandler, Nov 28 2003

EXTENSIONS

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

STATUS

approved

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