A102342 -id:A102342 - cp's OEIS frontend

A139367 a(n) = A102700(n) - A102342(n).

1, 1, 2, 3, 2, 1, 3, 2, 4, 4, 6, 4, 4, 9, 8, 7, 7, 7, 7, 7, 5, 2, 3, 2, 2, 4, 4, 7, 10, 10, 9, 9, 8, 7, 5, 6, 9, 7, 13, 13, 13, 11, 12, 14, 15, 23, 16, 16, 16, 10, 10, 16, 13, 13, 13, 13, 12, 7, 10, 7, 1, 1, 1, 4, 6, 5, 9, 9, 13, 11, 16, 13, 13, 15, 13, 8, 9, 8, 10, 9, 10, 6, 7, 7, 10, 10, 11, 18

Offset: 1

Juri-Stepan Gerasimov, Jun 09 2008

sign

a(332) = -1.

Index entries for prime races

From R. J. Mathar, Apr 25 2010: (Start)
A102700 := proc(n) option remember; if n = 1 then 1; else for a from procname(n-1)+1 do if isprime(10*a+9) then return a; end if; end do: end if; end proc:
A102342 := proc(n) option remember; if n = 1 then 0; else for a from procname(n-1)+1 do if isprime(10*a+7) then return a; end if; end do: end if; end proc:
A139367 := proc(n) A102700(n)-A102342(n) ; end proc: seq(A139367(n),n=1..120) ; (End)

Corrected (a 6 replaced by 7, a 7 by 9, a 13 by 16) and extended by R. J. Mathar, Apr 25 2010

A139368 a(n) = A024912(n) - A102342(n).

Original entry on oeis.org

1, 2, 1, 2, 1, 1, 3, 3, 5, 4, 5, 5, 3, 2, 1, 1, 2, 7, 8, 7, 7, 4, 6, 6, 3, 5, 6, 6, 6, 8, 6, 8, 4, 6, 4, 9, 9, 9, 10, 11, 12, 10, 11, 10, 12, 16, 9, 9, 9, 5, 8, 7, 5, 7, 8, 13, 11, 6, 7, 5, 1, 1, 2, 10, 11, 15, 15, 14, 12, 10, 12, 9, 9, 14, 18, 13, 14, 13, 14, 14, 12, 8, 8, 8, 7, 8, 4, 6, 7, 11, 10

Offset: 1

Juri-Stepan Gerasimov, Jun 09 2008

sign

A139368(219) = -4.

Index entries for prime races

From R. J. Mathar, Apr 25 2010: (Start)
A102342 := proc(n) option remember; if n = 1 then 0; else for a from procname(n-1)+1 do if isprime(10*a+7) then return a; end if; end do: end if; end proc:
A024912 := proc(n) option remember; if n = 1 then 1; else for a from procname(n-1)+1 do if isprime(10*a+1) then return a; end if; end do: end if; end proc:
A139368 := proc(n) A024912(n)-A102342(n) ; end proc: seq(A139368(n),n=1..120) ; (End)

More terms from R. J. Mathar, Apr 25 2010

A030432 Primes of form 10n+7.

Original entry on oeis.org

7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577, 587, 607, 617, 647, 677, 727, 757, 787, 797, 827, 857, 877, 887, 907, 937, 947, 967, 977, 997, 1087, 1097, 1117, 1187, 1217, 1237

Offset: 1

Warut Roonguthai

Union of A132231 and A039949. - Ray Chandler, Apr 07 2009
5 is not quadratic residue of primes of this form. - Vincenzo Librandi, Jun 25 2014
Also primes of the form 5n+2 with positive n. - Danny Rorabaugh, Feb 20 2016
Intersection of A000040 and A017353. - Iain Fox, Dec 30 2017

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.

Cf. A030430 (10n+1), A030431 (10n+3), A030433 (10n+9).

Cf. A045357, A045380, A049509, A102342.

[n: n in [7..1240 by 10] | IsPrime(n)]; // Bruno Berselli, Apr 06 2011

Select[Prime@Range[210], Mod[ #, 10] == 7 &] (* Ray Chandler, Nov 07 2006 *)

is(n)=n%10==7 && isprime(n) \\ Charles R Greathouse IV, Jul 01 2013

lista(nn) = forprime(p=7, nn, if(p%10==7, print1(p, ", "))) \\ Iain Fox, Dec 30 2017

[10*n+7 for n in range(124) if is_prime(10*n+7)] # Danny Rorabaugh, Feb 20 2016

a(n) = 10*A102342(n) + 7.

a(n) ~ 4n log n. - Charles R Greathouse IV, Jul 01 2013

Extended by Ray Chandler, Nov 07 2006

A007811 Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes.

Original entry on oeis.org

1, 10, 19, 82, 148, 187, 208, 325, 346, 565, 943, 1300, 1564, 1573, 1606, 1804, 1891, 1942, 2101, 2227, 2530, 3172, 3484, 4378, 5134, 5533, 6298, 6721, 6949, 7222, 7726, 7969, 8104, 8272, 8881, 9784, 9913, 10111, 10984, 11653, 11929, 12220, 13546, 14416, 15727

Offset: 1

N. J. A. Sloane and J. H. Conway, Mar 15 1996

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A024912, A102338, A102342, A102700, A007530, A014561, A008471, A032352, A216292, A216293, A125855.

Cf. A010051, A245304, A245305.

a007811 n = a007811_list !! (n-1)
a007811_list = map (pred . head) $ filter (all (== 1) . map a010051') $
   iterate (zipWith (+) [10, 10, 10, 10]) [1, 3, 7, 9]
-- Reinhard Zumkeller, Jul 18 2014

[n: n in [0..10000] | forall{10*n+r: r in [1,3,7,9] | IsPrime(10*n+r)}]; // Bruno Berselli, Sep 04 2012

for n from 1 to 10000 do m := 10*n: if isprime(m+1) and isprime(m+3) and isprime(m+7) and isprime(m+9) then print(n); fi: od: quit

Select[ Range[ 1, 10000, 3 ], PrimeQ[ 10*#+1 ] && PrimeQ[ 10*#+3 ] && PrimeQ[ 10*#+7 ] && PrimeQ[ 10*#+9 ]& ]
Select[Range[15000], And @@ PrimeQ /@ ({1, 3, 7, 9} + 10#) &] (* Ray Chandler, Jan 12 2007 *)

p=2;q=3;r=5;forprime(s=7,1e5,if(s-p==8 && r-p==6 && q-p==2 && p%10==1, print1(p", ")); p=q;q=r;r=s) \\ Charles R Greathouse IV, Mar 21 2013

use ntheory ":all"; my @s = map { ($-1)/10 } sieve_prime_cluster(10,1e9, 2,6,8); say for @s; # _Dana Jacobsen, May 04 2017

a(n) = 3*A014561(n) + 1. - Zak Seidov, Sep 21 2009

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

A023239 Primes p such that 10*p + 7 is also prime.

Original entry on oeis.org

3, 13, 19, 31, 61, 67, 79, 97, 109, 127, 163, 199, 223, 229, 241, 277, 283, 313, 367, 379, 421, 433, 439, 463, 487, 523, 541, 547, 571, 619, 631, 673, 691, 751, 757, 787, 811, 823, 829, 853, 859, 883, 937, 967, 1033, 1093, 1117, 1171, 1237, 1249, 1291, 1303, 1321

Offset: 1

David W. Wilson

nonn

John Cerkan, Table of n, a(n) for n = 1..10000

Cf. A023238.

Subsequence of A102342.

[n: n in [0..1000] | IsPrime(n) and IsPrime(10*n+7)] // Vincenzo Librandi, Nov 20 2010

Select[Prime[Range[200]], PrimeQ[10# + 7] &] (* Alonso del Arte, Jun 24 2014 *)

a(n) == 1 (mod 6), for n > 1. - John Cerkan, Sep 12 2016

A126785 Numbers k such that 10*k + 11 is prime.

Original entry on oeis.org

0, 2, 3, 5, 6, 9, 12, 14, 17, 18, 20, 23, 24, 26, 27, 30, 32, 39, 41, 42, 45, 48, 51, 53, 56, 59, 62, 63, 65, 68, 69, 74, 75, 80, 81, 87, 90, 93, 96, 98, 101, 102, 104, 105, 108, 114, 116, 117, 119, 122, 128, 129, 131, 135, 137, 144, 146, 147, 150, 152, 156, 159, 161

Offset: 1

Parthasarathy Nambi, Feb 18 2007

			If n=98 then 10n + 11 = 991 (prime).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A102342.

[ n: n in [0..200] | IsPrime(10*n+11) ]; // Vincenzo Librandi, Nov 23 2010

select(n -> isprime(10*n+11), [$0..500]); # Robert Israel, Jan 10 2019

Select[Range[0,161],PrimeQ[10#+11]&] (* James C. McMahon, Dec 27 2024 *)

is(n)=isprime(10*n+11) \\ Charles R Greathouse IV, Jun 13 2017

A124825 Numbers k such that 10k + 7 and 7k + 10 are primes.

Original entry on oeis.org

1, 3, 9, 13, 27, 31, 33, 39, 57, 67, 79, 87, 93, 109, 111, 121, 159, 163, 169, 177, 187, 223, 229, 237, 241, 267, 277, 303, 351, 363, 367, 369, 379, 387, 421, 433, 439, 451, 463, 493, 507, 519, 523, 541, 571, 573, 589, 603, 621, 633, 639, 663, 673, 697, 699

Offset: 1

Zak Seidov, Nov 09 2006

nonn

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

Intersection of A102342 and A111250. - Michel Marcus, Jan 22 2018

[n: n in [0..700] | IsPrime(10*n+7) and IsPrime(7*n+10)] // Vincenzo Librandi, Mar 26 2010

Select[Range[700],AllTrue[{10#+7,7#+10},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 05 2019 *)

A024914 Numbers k such that 10*k - 3 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 10, 11, 13, 14, 16, 17, 20, 23, 26, 28, 31, 32, 34, 35, 37, 40, 46, 47, 49, 55, 56, 58, 59, 61, 62, 65, 68, 73, 76, 79, 80, 83, 86, 88, 89, 91, 94, 95, 97, 98, 100, 109, 110, 112, 119, 122, 124, 128, 130, 131, 133, 137, 143, 145, 149, 157, 160, 161, 163, 164, 166, 167

Offset: 1

Clark Kimberling

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

[n: n in [1..200] |IsPrime(10*n-3)]; // Vincenzo Librandi, Nov 19 2010

select(k->isprime(10*k-3),[$1..170]); # Muniru A Asiru, Jul 15 2018

Select[Range[200], PrimeQ[10#-3]&] (* Harvey P. Dale, Nov 22 2012 *)

is(n)=isprime(10*n-3) \\ Charles R Greathouse IV, Jun 06 2017

a(n) = 1 + A102342(n). - R. J. Mathar, Sep 25 2013

A153308 Numbers n such that 10*n+7 is not prime.

Original entry on oeis.org

2, 5, 7, 8, 11, 14, 17, 18, 20, 21, 23, 24, 26, 28, 29, 32, 35, 37, 38, 40, 41, 42, 43, 44, 47, 49, 50, 51, 52, 53, 56, 59, 62, 63, 65, 66, 68, 69, 70, 71, 73, 74, 76, 77, 80, 81, 83, 84, 86, 89, 91, 92, 95, 98, 100, 101, 102, 103, 104, 105, 106, 107

Offset: 1

Vincenzo Librandi, Dec 23 2008

			Distribution of the terms in the following triangular array:
*;
*,*;
*,*,*;
2,*,*,*;
*,*,7,*,*;
*,*,*,11,*,*;
*,*,*,*,*,*,*;
*,*,*,*,18,*,*,*;
5,*,*,*,*,24,*,*,*;
*,*,14,*,*,*,*,35,*,*;
*,*,*,20,*,*,*,*,43,*,*;etc.
where * marks the non-integer values of (2*h*k + k + h - 3)/5 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013

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

A102342.

[n: n in [0..150] | not IsPrime(10*n + 7)]; // Vincenzo Librandi, Jan 12 2013

Select[Range[0, 200], !PrimeQ[10*# + 7]&] (* Vincenzo Librandi, Jan 12 2013 *)

cp's OEIS Frontend

A139367 a(n) = A102700(n) - A102342(n).

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Maple

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A139368 a(n) = A024912(n) - A102342(n).

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Maple

Extensions

A030432 Primes of form 10n+7.

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Magma

Mathematica

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PARI

Sage

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A007811 Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes.

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Haskell

Magma

Maple

Mathematica

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Perl

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

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Mathematica

Formula

Extensions

A023239 Primes p such that 10*p + 7 is also prime.

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Keywords

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Crossrefs

Programs

Magma

Mathematica

Formula

A126785 Numbers k such that 10*k + 11 is prime.

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Examples

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Programs

Magma

Maple

Mathematica

PARI