A039949 -id:A039949 - cp's OEIS frontend

A030432 Primes of form 10n+7.

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

A132230 Primes congruent to 1 (mod 30).

Original entry on oeis.org

31, 61, 151, 181, 211, 241, 271, 331, 421, 541, 571, 601, 631, 661, 691, 751, 811, 991, 1021, 1051, 1171, 1201, 1231, 1291, 1321, 1381, 1471, 1531, 1621, 1741, 1801, 1831, 1861, 1951, 2011, 2131, 2161, 2221, 2251, 2281, 2311, 2341, 2371, 2521, 2551, 2671

Offset: 1

Omar E. Pol, Aug 15 2007

Also primes congruent to 1 (mod 15). - N. J. A. Sloane, Jul 11 2008

Primes ending in 1 with (SOD-1)/3 integer where SOD is sum of digits. - Ki Punches, Feb 04 2009

			From _Muniru A Asiru_, Nov 01 2017: (Start)
31 is a prime and 31 = 30*1 + 1;
61 is a prime and 61 = 30*2 + 1;
151 is a prime and 151 = 30*5 + 1;
211 is a prime and 211 = 30*7 + 1;
241 is a prime and 241 = 30*8 + 1;
271 is a prime and 271 = 30*9 + 1.
(End)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A057204, A068228, A129805, A039949, A132231-A132236.

A132230 := Filtered(Filtered([1..10^6], n -> n mod 30 = 1), IsPrime); # Muniru A Asiru, Nov 01 2017

select(isprime, [seq(i,i=1..1000,30)]); # Robert Israel, Jan 19 2016

Select[Range[1, 3000, 30], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2012 *)
Select[Prime[Range[400]],Mod[#,30]==1&] (* Harvey P. Dale, May 21 2021 *)

is(n)=isprime(n) && n%30==1 \\ Charles R Greathouse IV, Jul 01 2016

a(n) = A111175(n)*30 + 1. - Ray Chandler, Apr 07 2009

Intersection of A030430 and A002476. - Ray Chandler, Apr 07 2009

Edited by Ray Chandler, Apr 07 2009

A132236 Primes congruent to 29 (mod 30).

Original entry on oeis.org

29, 59, 89, 149, 179, 239, 269, 359, 389, 419, 449, 479, 509, 569, 599, 659, 719, 809, 839, 929, 1019, 1049, 1109, 1229, 1259, 1289, 1319, 1409, 1439, 1499, 1559, 1619, 1709, 1889, 1949, 1979, 2039, 2069, 2099, 2129, 2309, 2339, 2399, 2459, 2549, 2579

Offset: 1

Omar E. Pol, Aug 15 2007

Primes ending in 9 with (SOD-1)/3 non-integer where SOD is sum of digits. - Ki Punches

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A039949, A132230-A132235.

[p: p in PrimesUpTo(3000) | p mod 30 eq 29 ]; // Vincenzo Librandi, Aug 14 2012

Select[Prime[Range[400]],Mod[#,30]==29&] (* Harvey P. Dale, Dec 25 2011 *)
Select[Prime[Range[1000]],MemberQ[{29},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)

is(n)=isprime(n) && n%30==29 \\ Charles R Greathouse IV, Jul 01 2016

a(n) = A158850(n)*30 + 29. - Chandler

Intersection of A030433 and A007528. - Chandler

Extended by Ray Chandler, Apr 07 2009

A132231 Primes congruent to 7 (mod 30).

Original entry on oeis.org

7, 37, 67, 97, 127, 157, 277, 307, 337, 367, 397, 457, 487, 547, 577, 607, 727, 757, 787, 877, 907, 937, 967, 997, 1087, 1117, 1237, 1297, 1327, 1447, 1567, 1597, 1627, 1657, 1747, 1777, 1867, 1987, 2017, 2137, 2287, 2347, 2377, 2437, 2467, 2557, 2617, 2647

Offset: 1

Omar E. Pol, Aug 15 2007

Primes ending in 7 with (SOD-1)/3 integer where SOD is sum of digits. - Ki Punches, Feb 07 2009
Intersection of A030432 and A002476. - Ray Chandler, Apr 07 2009
Only from 4927 on, there are more composite numbers than primes in {7+30k}, see A227869. - M. F. Hasler, Nov 02 2013
Terms are non-twin primes A007510, except for 7. - Jonathan Sondow, Oct 27 2017

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages
Omar E. Pol, Prime numbers in a sieve with 30 columns
Omar E. Pol, Sobre el patrón de los números primos

Cf. A007510, A007528, A010051, A068229, A117047, A129807, A039949, A132230-A132236, A214360.

a132231 n = a132231_list !! (n-1)
a132231_list = [x | k <- [0..], let x = 30 * k + 7, a010051' x == 1]
-- Reinhard Zumkeller, Jul 13 2012

[p: p in PrimesUpTo(3000) | p mod 30 eq 7 ]; // Vincenzo Librandi, Aug 14 2012

Select[30*Range[0,100]+7,PrimeQ] (* Harvey P. Dale, Feb 01 2012 *)
Select[Prime[Range[1000]],MemberQ[{7},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)

forstep(p=7,1999,30,isprime(p)&&print1(p",")) \\ M. F. Hasler, Nov 02 2013

a(n) = A158573(n)*30 + 7. - Ray Chandler, Apr 07 2009

a(n) = A211890(4,n-1) for n <= 5. - Reinhard Zumkeller, Jul 13 2012

Extended by Ray Chandler, Apr 07 2009

A132232 Primes congruent to 11 (mod 30).

Original entry on oeis.org

11, 41, 71, 101, 131, 191, 251, 281, 311, 401, 431, 461, 491, 521, 641, 701, 761, 821, 881, 911, 941, 971, 1031, 1061, 1091, 1151, 1181, 1301, 1361, 1451, 1481, 1511, 1571, 1601, 1721, 1811, 1871, 1901, 1931, 2081, 2111, 2141, 2351, 2381, 2411, 2441, 2531

Offset: 1

Omar E. Pol, Aug 15 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A068231, A039949.

Cf. A132230, A132231, A132233, A132234, A132235, A132236.

[p: p in PrimesUpTo(3000) | p mod 30 eq 11 ]; // Vincenzo Librandi, Aug 14 2012

Select[Prime[Range[1000]],MemberQ[{11},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)
Select[Range[11,2600,30],PrimeQ] (* Harvey P. Dale, Mar 07 2020 *)

is(n)=isprime(n) && n%30==11 \\ Charles R Greathouse IV, Jul 01 2016

From Ray Chandler, Apr 07 2009: (Start)
a(n) = A158614(n)*30 + 11.
Intersection of A030430 and A007528. (End)

Extended by Ray Chandler, Apr 07 2009

A132235 Primes congruent to 23 (mod 30).

Original entry on oeis.org

23, 53, 83, 113, 173, 233, 263, 293, 353, 383, 443, 503, 563, 593, 653, 683, 743, 773, 863, 953, 983, 1013, 1103, 1163, 1193, 1223, 1283, 1373, 1433, 1493, 1523, 1553, 1583, 1613, 1733, 1823, 1913, 1973, 2003, 2063, 2153, 2213, 2243, 2273, 2333, 2393

Offset: 1

Omar E. Pol, Aug 15 2007

Primes (excluding 3) ending in 3 with (SOD-1)/3 non-integer where SOD is sum of digits. - Ki Punches
The sequence is infinite by Dirichlet's theorem. - Arkadiusz Wesolowski, Apr 02 2014
Terms are non-twin primes A007510. - Omar E. Pol, Jul 25 2019

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Omar E. Pol, Prime numbers in a sieve with 30 columns

Cf. A000040, A039949.

Cf. A132230, A132231, A132232, A132233, A132234, A132236.

[p: p in PrimesUpTo(3000) | p mod 30 eq 23 ]; // Vincenzo Librandi, Aug 14 2012

Select[Prime[Range[1000]],MemberQ[{23},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)
Select[Range[23,2400,30],PrimeQ] (* Harvey P. Dale, Jan 27 2020 *)

is(n)=isprime(n) && n%30==23 \\ Charles R Greathouse IV, Jul 01 2016

a(n) = A158791(n)*30 + 23. - Ray Chandler, Apr 07 2009

Intersection of A030431 and A007528. - Ray Chandler, Apr 07 2009

Extended by Ray Chandler, Apr 07 2009

A132233 Primes congruent to 13 (mod 30).

Original entry on oeis.org

13, 43, 73, 103, 163, 193, 223, 283, 313, 373, 433, 463, 523, 613, 643, 673, 733, 823, 853, 883, 1033, 1063, 1093, 1123, 1153, 1213, 1303, 1423, 1453, 1483, 1543, 1663, 1693, 1723, 1753, 1783, 1873, 1933, 1993, 2053, 2083, 2113, 2143, 2203, 2293, 2383

Offset: 1

Omar E. Pol, Aug 15 2007

Primes ending in 3 with (SOD-1)/3 integer where SOD is sum of digits. - Ki Punches

Subsequence of primes of A082369. - Michel Marcus, Jan 23 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A039949, A082369, A132230-A132236.

[p: p in PrimesUpTo(3000) | p mod 30 eq 13 ]; // Vincenzo Librandi, Aug 14 2012

select(isprime, [seq(30*i+13,i=0..1000)]); # Robert Israel, Jan 24 2016

Select[Prime[Range[1000]],MemberQ[{13},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)

lista(nn) = forprime(p=2, nn, if(p % 30 == 13, print1(p, ", "))); \\ Altug Alkan, Jan 23 2016

a(n) = A158746(n)*30 + 13. - Ray Chandler, Apr 07 2009

Intersection of A030431 and A002476. - Ray Chandler, Apr 07 2009

Extended by Ray Chandler, Apr 07 2009

A132234 Primes congruent to 19 (mod 30).

Original entry on oeis.org

19, 79, 109, 139, 199, 229, 349, 379, 409, 439, 499, 619, 709, 739, 769, 829, 859, 919, 1009, 1039, 1069, 1129, 1249, 1279, 1399, 1429, 1459, 1489, 1549, 1579, 1609, 1669, 1699, 1759, 1789, 1879, 1999, 2029, 2089, 2179, 2239, 2269, 2389, 2539, 2659, 2689

Offset: 1

Omar E. Pol, Aug 15 2007

Also primes congruent to 4 (mod 15). - N. J. A. Sloane, Jul 11 2008

Primes ending in 9 with (SOD-1)/3 integer where SOD is sum of digits. - Ki Punches

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A039949, A132230-A132236.

[p: p in PrimesUpTo(3000) | p mod 30 eq 19 ]; // Vincenzo Librandi, Aug 14 2012

Select[Prime[Range[1000]],MemberQ[{19},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)
Select[Range[19,2700,30],PrimeQ] (* Harvey P. Dale, Dec 26 2014 *)

is(n)=isprime(n) && n%30==19 \\ Charles R Greathouse IV, Jul 01 2016

a(n) = A158806(n)*30 + 19. - Chandler

Intersection of A030433 and A002476. - Chandler

Extended by Ray Chandler, Apr 07 2009

A158648 Numbers n such that 30*n + 17 is prime.

Original entry on oeis.org

0, 1, 3, 4, 5, 6, 7, 8, 10, 11, 15, 18, 19, 20, 21, 22, 26, 27, 28, 29, 31, 32, 36, 39, 40, 42, 43, 45, 47, 49, 53, 54, 55, 56, 59, 61, 62, 63, 66, 67, 69, 73, 74, 75, 76, 78, 80, 81, 82, 88, 89, 92, 94, 96, 97, 98, 104, 105, 108, 111, 113, 115, 117, 118, 120, 122, 125, 126

Offset: 1

Ki Punches, Mar 23 2009

nonn

Encoded primes with LSD 7 and (SOD-1)/3 non-integer, (LSD, least significant digit; SOD, sum of digits). Divide any such number by 30, if the whole number portion of the quotient is in the sequence, the number is prime.

			Example: 3557, with LSD 7 and (SOD-1)/3 = 6.333 (non-integer); Then 7557/30 = 118.566, or 118 which is in the sequence, and thus 3557 is prime.

Cf. A111175, A158573, A158614, A158746, A158791, A158806, A158850.

Select[Range[0,200],PrimeQ[30#+17]&] (* Harvey P. Dale, Mar 21 2018 *)

is(n)=isprime(30*n+17) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A039949(n) - 17)/30 = Floor[A039949(n)/30]. - Chandler

Edited by Ray Chandler, Apr 07 2009

A106859 Primes of the form 2x^2 + xy + 2y^2.

Original entry on oeis.org

2, 3, 5, 17, 23, 47, 53, 83, 107, 113, 137, 167, 173, 197, 227, 233, 257, 263, 293, 317, 347, 353, 383, 443, 467, 503, 557, 563, 587, 593, 617, 647, 653, 677, 683, 743, 773, 797, 827, 857, 863, 887, 947, 953, 977, 983, 1013, 1097, 1103, 1163, 1187, 1193

Offset: 1

T. D. Noe, May 09 2005

Discriminant=-15.
If p is a prime >= 17 in this sequence then k==0 (mod 4) for all k satisfying "B(2k)(p^k-1) is an integer" where B are the Bernoulli numbers. - Benoit Cloitre, Nov 14 2005
Equals {2, 3, 5 and primes congruent to 17, 23 (mod 30)}; see A039949 and A132235. Except for 2, the same as primes of the form 3x^2 + 5y^2, which has discriminant -60. - T. D. Noe, May 02 2008
Equals {3, 5 and primes congruent to 2, 8 (mod 15)} sorted; see A033212. This form is in the only non-principal class (respectively, genus) for fundamental discriminant -15. - Rick L. Shepherd, Jul 25 2014 [See A343241 for the 2, 8 (mod 15) primes.]
From Wolfdieter Lang, Jun 08 2021: (Start)
Regarding the above comment of T. D. Noe on the form [3, 0, 5]: the class number h(-60) = 2 = A000003(15), and [1, 0, 15] is the principal reduced form, representing the primes given in A033212.
The form [3, 0, 5] represents the proper equivalence class of the second genus of forms of discriminant Disc = -60. The Legendre symbol for the odd primes, not 3 or 5, satisfy L(-3|p) = -1 and L(5|p) = -1, leading to primes p == {17, 23, 47, 53} (mod 60). See the Buell reference, p. 52, for the two characters L(p|3) and L(p|5). The prime 2 is represented by the imprimitive reduced form [2, 2, 8] of Disc = -60. (End)

D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 51-52.

Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 2000 terms from Vincenzo Librandi, next 691 terms from N. J. A. Sloane]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Cf. A000003, A139827, A039949, A132235, A033212, A343241.

QuadPrimes2[2, 1, 2, 100000] (* see A106856 *)

{ fc(a,b,c,M) = my(p,t1,t2,n); t1 = listcreate();
for(n=1,M, p = prime(n);
t2 = qfbsolve(Qfb(a,b,c),p); if(t2 == 0,, listput(t1,p)));
print(t1);
}
fc(2,1,2,1000); \\ N. J. A. Sloane, Jun 06 2014

Removed defective Mma program and extended the b-file using the PARI program fc. - N. J. A. Sloane, Jun 06 2014

cp's OEIS Frontend

A030432 Primes of form 10n+7.

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A132230 Primes congruent to 1 (mod 30).

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A132236 Primes congruent to 29 (mod 30).

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A132231 Primes congruent to 7 (mod 30).

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A132232 Primes congruent to 11 (mod 30).

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A132235 Primes congruent to 23 (mod 30).

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