A141860 -id:A141860 - cp's OEIS frontend

A039949 Primes of the form 30n - 13.

17, 47, 107, 137, 167, 197, 227, 257, 317, 347, 467, 557, 587, 617, 647, 677, 797, 827, 857, 887, 947, 977, 1097, 1187, 1217, 1277, 1307, 1367, 1427, 1487, 1607, 1637, 1667, 1697, 1787, 1847, 1877, 1907, 1997, 2027, 2087, 2207, 2237, 2267, 2297, 2357, 2417

Offset: 1

Felice Russo

This linear form produces the most primes for n between 1 and 1000 (411/1000).
Primes congruent to 17 (mod 30). - Omar E. Pol, Aug 15 2007
Primes ending in 7 with (SOD-1)/3 non-integer where SOD is sum of digits. - Ki Punches
Or primes p such that (p mod 3) = (p mod 5) and (p mod 2) <> (p mod 3), (p > 2). - Mikk Heidemaa, Jan 19 2016

C. Clawson, Mathematical Mysteries, Plenum Press, 1996, p. 173

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

Cf. A132230-A132236, A141860.

[p: p in PrimesUpTo(3000) | p mod 30 in [17]]; // Vincenzo Librandi, Aug 04 2012

Select[Prime[Range[1000]],MemberQ[{17},Mod[#,30]]&] (* Vincenzo Librandi, Aug 04 2012 *)
Select[Range[17,3000,30],PrimeQ] (* Zak Seidov, Apr 15 2015 *)

select(n->n%30==17, primes(500)) \\ Charles R Greathouse IV, Apr 28 2015

a(n) = A158648(n)*30 + 17. - Ray Chandler, Apr 07 2009
Intersection of A030432 and A007528. - Ray Chandler, Apr 07 2009
a(n) = A141860(n+1). - Zak Seidov, Apr 15 2015

Extended by Ray Chandler, Apr 07 2009

A267540 Primes p such that p (mod 3) = p (mod 5).

Original entry on oeis.org

2, 17, 31, 47, 61, 107, 137, 151, 167, 181, 197, 211, 227, 241, 257, 271, 317, 331, 347, 421, 467, 541, 557, 571, 587, 601, 617, 631, 647, 661, 677, 691, 751, 797, 811, 827, 857, 887, 947, 977, 991, 1021, 1051, 1097, 1171, 1187, 1201, 1217, 1231, 1277, 1291

Offset: 1

Mikk Heidemaa, Jan 16 2016

Or primes p such that p (mod 15) = {1, 2}.
Terminal digits in a(7)...a(32) alternate 26 times (7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1). 25 differences between the 2 consecutive terms in this range show patterns as well.
A differenceroot function can generate the terms a(7)...a(32).

Cf. A063118, A141860, A216145.

[p: p in PrimesUpTo(2000) | p mod 3 eq p mod 5]; // Vincenzo Librandi, Jan 17 2016

select(isprime, [seq(seq(15*i+j, j= 1..2), i=0..10000)]); # Robert Israel, Jan 17 2016

Select[ Prime[ Range[10000]], (Mod[#,3] == Mod[#,5]) &] (* Or *)
Select[ Prime[ Range[10000]], 0 < Mod[#,15] < 3 &]

lista(nn) = forprime(p=2, nn, if(p%3 == p%5, print1(p, ", "))); \\ Altug Alkan, Jan 17 2016

a(n) = 1/2*((-1)^n*(3*(-1)^n*(10n+81)-1)) with (1

G.f.: (x*(-14x^6-32x^5+16x^4+30x^3-x+14)+17)/((x-1)^2*(x+1)) generates a(2)...a(16), (0<=x<15).

G.f.: (x*(x*(30x*(-2x^4-x^3+x+2)-301)+14)+317)/((x-1)^2*(x+1)) generates a(17)...a(32), (0<=x<16).

More terms from Vincenzo Librandi, Jan 17 2016

A220081 Primes of the form 15k^2 - 15k + 17.

Original entry on oeis.org

17, 47, 107, 197, 317, 467, 647, 857, 1097, 1367, 1667, 1997, 2357, 3167, 3617, 5147, 5717, 6317, 6947, 7607, 8297, 9767, 12197, 13967, 14897, 18917, 19997, 21107, 22247, 23417, 25847, 27107, 29717, 33857, 36767, 41357, 51347, 53117, 54917, 56747, 60497

Offset: 1

Vincenzo Librandi, Dec 17 2012

The formula gives consecutive primes for k from 0 to 13.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Cf. A000040, A005846, A156252.

Subsequence of A030432, A039949, A141860.

[a: n in [1..100] | IsPrime(a) where a is 15*n^2 - 15*n + 17 ];

Select[Table[15 n^2 - 15 n + 17, {n, 1, 100}], PrimeQ]

A247089 Initial members of prime quadruples (p, p+2, p+30, p+32).

Original entry on oeis.org

11, 29, 41, 71, 107, 149, 197, 239, 281, 431, 569, 827, 1019, 1031, 1061, 1289, 1451, 1667, 1997, 2081, 2111, 2237, 2309, 2657, 2969, 3299, 3329, 3359, 3527, 3821, 4019, 4127, 4229, 4241, 4517, 5849, 6269, 6659, 6761, 7457, 7559, 8597

Offset: 1

Karl V. Keller, Jr., Jan 10 2015

nonn

Primes p such that (p, p+2) and (p+30, p+32) are twin prime pairs.
This sequence is a subsequence of A001359 (lesser of twin primes).
The subset of terms ending in 1 in this sequence is a subsequence of A132232 (primes, 11 mod 30).
The subset of terms ending in 7 in this sequence is a subsequence of A141860 (primes, 2 mod 15).
The subset of terms ending in 9 in this sequence is a subsequence of A132236 (primes, 29 mod 30).

			For n=11, the numbers 11, 13, 41, 43, are primes.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..100000
Eric Weisstein's World of Mathematics, Prime Quadruplet.
Eric Weisstein's World of Mathematics, Twin Primes
Wikipedia, Twin prime

Cf. A077800 (twin primes), A001359, A132232, A132236, A141860, A181603 (twins, end 1), A181605 (twins, end 7), A181606 (twins, end 9).

a247089[n_] := Select[Prime@ Range@ n, And[PrimeQ[# + 2], PrimeQ[# + 30], PrimeQ[# + 32]] &]; a247089[1100] (* Michael De Vlieger, Jan 11 2015 *)

from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+30) and isprime(n+32): print(n,end=', ')

Showing 1-4 of 4 results.

cp's OEIS Frontend

A039949 Primes of the form 30n - 13.

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A267540 Primes p such that p (mod 3) = p (mod 5).

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A220081 Primes of the form 15*k^2 - 15*k + 17.

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A247089 Initial members of prime quadruples (p, p+2, p+30, p+32).

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A220081 Primes of the form 15k^2 - 15k + 17.