A049511 -id:A049511 - cp's OEIS frontend

A030430 Primes of the form 10*n+1.

11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 401, 421, 431, 461, 491, 521, 541, 571, 601, 631, 641, 661, 691, 701, 751, 761, 811, 821, 881, 911, 941, 971, 991, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1181, 1201, 1231, 1291

Offset: 1

Warut Roonguthai

Also primes of form 5*n+1 or equivalently 5*n+6.
Primes p such that the arithmetic mean of divisors of p^4 is an integer: A000203(p^4)/A000005(p^4) = C. - Ctibor O. Zizka, Sep 15 2008
Being a subset of A141158, this is also a subset of the primes of form x^2-5*y^2. - Tito Piezas III, Dec 28 2008
5 is quadratic residue of primes of this form. - Vincenzo Librandi, Jun 25 2014
Primes p such that 5 divides sigma(p^4), cf. A274397. - M. F. Hasler, Jul 10 2016

Michael B. Porter, Table of n, a(n) for n = 1..100000
A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.
Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 519.
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 5.

Cf. A024912, A045453, A049511, A081759, A017281, A010051, A004615 (multiplicative closure).
Cf. A001583 (subsequence).
Union of A132230 and A132232. - Ray Chandler, Apr 07 2009

a030430 n = a030430_list !! (n-1)
a030430_list = filter ((== 1) . a010051) a017281_list
-- Reinhard Zumkeller, Apr 16 2012

Select[Prime@Range[210], Mod[ #, 10] == 1 &] (* Ray Chandler, Dec 06 2006 *)
Select[Range[11,1291,10],PrimeQ] (*Zak Seidov, Aug 14 2011*)

is(n)=n%10==1 && isprime(n) \\ Charles R Greathouse IV, Sep 06 2012

lista(nn) = forprime(p=11, nn, if(p%10==1, print1(p, ", "))) \\ Iain Fox, Dec 30 2017

a(n) = 10*A024912(n)+1 = 5*A081759(n)+6.
A104146(floor(a(n)/10)) = 1.
Union of A132230 and A132232. - Ray Chandler, Apr 07 2009
a(n) ~ 4n log n. - Charles R Greathouse IV, Sep 06 2012
Intersection of A000040 and A017281. - Iain Fox, Dec 30 2017

A024912 Numbers k such that 10*k + 1 is prime.

Original entry on oeis.org

1, 3, 4, 6, 7, 10, 13, 15, 18, 19, 21, 24, 25, 27, 28, 31, 33, 40, 42, 43, 46, 49, 52, 54, 57, 60, 63, 64, 66, 69, 70, 75, 76, 81, 82, 88, 91, 94, 97, 99, 102, 103, 105, 106, 109, 115, 117, 118, 120, 123, 129, 130, 132, 136, 138, 145, 147, 148, 151, 153, 157, 160, 162

Offset: 1

Clark Kimberling

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A030430, A049511, A081759.

[n: n in [1..1000] |IsPrime(10*n+1)]; // Vincenzo Librandi, Nov 19 2010

Select[Range[170], PrimeQ[10# + 1] &] (* Ray Chandler, Dec 06 2006 *)

is(n)=isprime(10*n+1) \\ Charles R Greathouse IV, Jul 02 2013

a(n) = (A081759(n)+1)/2.

A081759 Numbers n such that 5n+6 is prime.

Original entry on oeis.org

1, 5, 7, 11, 13, 19, 25, 29, 35, 37, 41, 47, 49, 53, 55, 61, 65, 79, 83, 85, 91, 97, 103, 107, 113, 119, 125, 127, 131, 137, 139, 149, 151, 161, 163, 175, 181, 187, 193, 197, 203, 205, 209, 211, 217, 229, 233, 235, 239, 245, 257, 259, 263, 271, 275, 289

Offset: 1

Giovanni Teofilatto, Nov 21 2003

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

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A024912, A030430, A049511, A067076, A087505, A089192, A089253.

[n: n in [0..300]| IsPrime(5*n + 6)]; // Vincenzo Librandi, Oct 16 2012

A081759 := proc(n) option remember: local k: if(n=1)then return 1: fi: for k from procname(n-1)+1 do if(isprime(5*k+6))then return k: fi: od: end: seq(A081759(n),n=1..100); # Nathaniel Johnston, May 28 2011

Select[Range[300], PrimeQ[5# + 6] &] (* Ray Chandler, Dec 06 2006 *)

is(n)=isprime(5*n+6) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = 2*A024912(n) - 1.

Corrected by Ray Chandler, Nov 22 2003

A049508 Numbers k such that prime(k) == 3 (mod 10).

Original entry on oeis.org

2, 6, 9, 14, 16, 21, 23, 27, 30, 38, 40, 44, 48, 51, 56, 61, 62, 65, 71, 74, 76, 84, 86, 90, 96, 99, 103, 108, 112, 117, 119, 122, 124, 130, 132, 137, 143, 147, 150, 153, 162, 166, 170, 174, 179, 183, 185, 188, 191, 192, 196, 198, 200, 208, 213, 220, 224, 227, 231

Offset: 1

J. Lowell

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Cf. A000720, A030431, A102338.

Cf. A049509, A049510, A049511.

Select[Range[240], Mod[Prime[ # ], 10] == 3 &] (* Ray Chandler, Nov 07 2006 *)

a(n) = A000720(A030431(n)). - Ray Chandler, Nov 07 2006

Edited and extended by Ray Chandler, Nov 07 2006

A049509 Numbers k such that prime(k) == 7 (mod 10).

Original entry on oeis.org

4, 7, 12, 15, 19, 25, 28, 31, 33, 37, 39, 45, 49, 55, 59, 63, 66, 68, 69, 73, 78, 88, 91, 93, 101, 102, 106, 107, 111, 113, 118, 123, 129, 134, 138, 139, 144, 148, 151, 154, 155, 159, 161, 163, 165, 168, 181, 184, 187, 195, 199, 203, 206, 211, 214, 217, 219, 225

Offset: 1

N. J. A. Sloane

nonn

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Cf. A000720, A030432, A102342.

Cf. A049508, A049510, A049511.

Select[Range[240], Mod[Prime[ # ], 10] == 7 &] (* Ray Chandler, Nov 07 2006 *)

a(n) = A000720(A030432(n)). - Ray Chandler, Nov 07 2006

Extended by Ray Chandler, Nov 07 2006

A049510 Numbers k such that prime(k) == 9 (mod 10).

Original entry on oeis.org

8, 10, 17, 22, 24, 29, 34, 35, 41, 46, 50, 52, 57, 70, 72, 75, 77, 80, 81, 85, 87, 92, 95, 97, 104, 109, 114, 120, 127, 128, 131, 136, 140, 145, 146, 149, 157, 158, 169, 171, 175, 176, 180, 186, 189, 201, 204, 205, 207, 209, 215, 222, 223, 226, 228, 232, 237, 239

Offset: 1

N. J. A. Sloane

nonn

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Cf. A000720, A030433, A102700.

Cf. A049508, A049509, A049511.

Select[Range[240], Mod[Prime[ # ], 10] == 9 &] (* Ray Chandler, Nov 07 2006 *)

a(n) = A000720(A030433(n)). - Ray Chandler, Nov 07 2006

Extended by Ray Chandler, Nov 07 2006

A088561 A088555 indexed by A000040.

Original entry on oeis.org

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

Offset: 1

Ray Chandler, Nov 28 2003

Subset of A049511.

Cf. A023219, A049511, A088555, A090161.

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

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

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

A269703 Numbers k such that prime(k) == 1 (mod 7).

Original entry on oeis.org

10, 14, 20, 30, 31, 45, 47, 52, 60, 68, 75, 82, 87, 90, 94, 101, 113, 115, 120, 122, 126, 132, 134, 144, 153, 156, 162, 163, 169, 177, 183, 192, 209, 213, 220, 226, 233, 239, 250, 251, 262, 267, 269, 288, 295, 304, 306, 315, 320, 324, 330, 337, 342, 344, 346

Offset: 1

Vincenzo Librandi, Mar 04 2016

nonn

The asymptotic density of this sequence is 1/6 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

			a(1) = 10 because prime(10) = 29 and 29 == 1 (mod 7).

The associated primes are in A004619.

Sequences of numbers n such that prime(n) == 1 (mod k): A091178 (k=3,6), A080147 (k=4), A049511 (k=5,10), this sequence (k=7), A269704 (k=8), A269705 (k=9).

[n: n in [1..500] | NthPrime(n) mod 7 eq 1];

Select[Range[500], Mod[Prime[#], 7] == 1 &]

lista(nn) = for(n=1, nn, if(Mod(prime(n),7)==1, print1(n, ", "))); \\ Altug Alkan, Mar 04 2016

a(n) ~ 6*n. - Charles R Greathouse IV, Sep 20 2016 [Corrected by Amiram Eldar, Mar 01 2021]

cp's OEIS Frontend

A030430 Primes of the form 10*n+1.

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A024912 Numbers k such that 10*k + 1 is prime.

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Magma

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A081759 Numbers n such that 5n+6 is prime.

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A049508 Numbers k such that prime(k) == 3 (mod 10).

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A049509 Numbers k such that prime(k) == 7 (mod 10).

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A049510 Numbers k such that prime(k) == 9 (mod 10).

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A088561 A088555 indexed by A000040.

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A269703 Numbers k such that prime(k) == 1 (mod 7).

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