A158648 -id:A158648 - 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

A111175 Numbers n such that 30*n + 1 is prime.

Original entry on oeis.org

1, 2, 5, 6, 7, 8, 9, 11, 14, 18, 19, 20, 21, 22, 23, 25, 27, 33, 34, 35, 39, 40, 41, 43, 44, 46, 49, 51, 54, 58, 60, 61, 62, 65, 67, 71, 72, 74, 75, 76, 77, 78, 79, 84, 85, 89, 91, 93, 95, 99, 100, 102, 104, 106, 109, 110, 111, 112, 113, 117, 118, 119, 121, 123, 131, 134, 135

Offset: 1

Parthasarathy Nambi, Oct 21 2005

nonn

Encoded primes with LSD 1 and (SOD-1)/3 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: 2671, with LSD 1 and (SOD-1)/3 = 2 (integer); Then 2671/30 = 89.033, or 89, which is in the sequence, and thus 2671 is prime. - Ki Punches, Mar 18 2009

			If n=99 then 30*n + 1 = 2971 (prime).

Cf. A158573, A158614, A158648, A158746, A158791, A158806, A158850.

is(n)=isprime(30*n+1) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A132230(n) - 1)/30 = Floor[A132230(n)/30]. - Chandler

Extended by Ray Chandler, Apr 07 2009

A158806 Numbers n such that 30*n + 19 is prime.

Original entry on oeis.org

0, 2, 3, 4, 6, 7, 11, 12, 13, 14, 16, 20, 23, 24, 25, 27, 28, 30, 33, 34, 35, 37, 41, 42, 46, 47, 48, 49, 51, 52, 53, 55, 56, 58, 59, 62, 66, 67, 69, 72, 74, 75, 79, 84, 88, 89, 90, 91, 100, 101, 102, 103, 105, 107, 108, 110, 115, 116, 117, 118, 123, 124, 125, 129, 130

Offset: 1

Ki Punches, Mar 27 2009

nonn

Encoded primes with LSD 9, (SOD-1)/3 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: 3019, with LSD 9, (SOD-1)/3 integer; Then 3019/30 = 100.633, or 100, which is in the sequence, thus 3019 is prime.

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

Cf. A111175, A158573, A158614, A158648, A158746, A158791, A158850.

Select[Range[0,150],PrimeQ[30#+19]&] (* Harvey P. Dale, Apr 05 2025 *)

is(n)=isprime(30*n+19) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A132234(n) - 19)/30 = Floor[A132234(n)/30]. - Chandler

Edited by Ray Chandler, Apr 07 2009

A158573 Numbers k such that 30*k + 7 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 24, 25, 26, 29, 30, 31, 32, 33, 36, 37, 41, 43, 44, 48, 52, 53, 54, 55, 58, 59, 62, 66, 67, 71, 76, 78, 79, 81, 82, 85, 87, 88, 89, 90, 92, 93, 95, 96, 97, 101, 102, 106, 107, 110, 115, 117, 118, 120, 121, 123, 124, 128

Offset: 1

Ki Punches, Mar 21 2009

nonn

Encoded primes with LSD 7 and (SOD-1)/3 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: 3877, with LSD 7 and (SOD-1)/3 = 23 (integer); Then 3877/30 = 129.233, or 129, which is in the sequence, and thus 3877 is prime.

Cf. A111175, A158614, A158648, A158746, A158791, A158806, A158850.

Select[Range[0,200],PrimeQ[30#+7]&] (* Harvey P. Dale, Jul 20 2018 *)

is(n)=isprime(30*n+7) \\ Charles R Greathouse IV, Mar 07 2016

a(n) = (A132231(n) - 7)/30 = floor(A132231(n)/30). - Ray Chandler, Apr 07 2009

a(n) ~ (4/15) n log n. - Charles R Greathouse IV, Mar 07 2016

Edited by Ray Chandler, Apr 07 2009

A158614 Numbers n such that 30*n + 11 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 9, 10, 13, 14, 15, 16, 17, 21, 23, 25, 27, 29, 30, 31, 32, 34, 35, 36, 38, 39, 43, 45, 48, 49, 50, 52, 53, 57, 60, 62, 63, 64, 69, 70, 71, 78, 79, 80, 81, 84, 86, 87, 90, 91, 93, 95, 100, 101, 106, 107, 108, 112, 115, 116, 119, 122, 123, 125, 127, 128

Offset: 1

Ki Punches, Mar 22 2009, Mar 29 2009

nonn

Encoded primes with LSD 1 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: 3191, with LSD 1 and (SOD-1)/3 = 4.33 (non-integer); Then 3191/30=106.367, or 106 which is in the sequence, thus 3191 is prime.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A111175, A158573, A158648, A158746, A158791, A158806, A158850.

Select[Range[0,130],PrimeQ[30#+11]&] (* Harvey P. Dale, Jul 26 2011 *)

is(n)=isprime(30*n+11) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A132232(n) - 11)/30 = floor(A132232(n)/30). - Ray Chandler, Apr 07 2009

Edited by Ray Chandler, Apr 07 2009

A158746 Numbers n such that 30*n + 13 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 9, 10, 12, 14, 15, 17, 20, 21, 22, 24, 27, 28, 29, 34, 35, 36, 37, 38, 40, 43, 47, 48, 49, 51, 55, 56, 57, 58, 59, 62, 64, 66, 68, 69, 70, 71, 73, 76, 79, 82, 83, 86, 89, 90, 93, 94, 98, 105, 108, 110, 111, 112, 114, 115, 119, 120, 121, 122, 124, 126, 127

Offset: 1

Ki Punches, Mar 25 2009

nonn

Encoded primes with LSD 3, (SOD-1)/3 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: 3163, with LSD 3 and (SOD-1)/3 = 4 (integer); Then 3163/30 = 105.433, or 105 which is in the sequence, thus 3163 is prime.

Cf. A111175, A158573, A158614, A158648, A158791, A158806, A158850.

Select[Range[0,200],PrimeQ[30#+13]&] (* Harvey P. Dale, Oct 16 2018 *)

is(n)=isprime(30*n+13) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A132233(n) - 13)/30 = Floor[A132233(n)/30]. - Chandler

Edited by Ray Chandler, Apr 07 2009

A158791 Numbers n such that 30*n + 23 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 24, 25, 28, 31, 32, 33, 36, 38, 39, 40, 42, 45, 47, 49, 50, 51, 52, 53, 57, 60, 63, 65, 66, 68, 71, 73, 74, 75, 77, 79, 80, 84, 87, 88, 89, 91, 94, 96, 98, 100, 102, 106, 110, 113, 117, 119, 120, 126, 127, 128, 130, 133

Offset: 1

Ki Punches, Mar 26 2009

nonn

Encoded primes with LSD 3 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: 3623, with LSD 3 and (SOD-1)/3 non-integer; Then 3623/30 = 120.766, or 120, which is in the sequence, thus 3623 is prime.

Cf. A111175, A158573, A158614, A158648, A158746, A158806, A158850.

Select[Range[0,200],PrimeQ[30#+23]&] (* Harvey P. Dale, Jul 31 2014 *)

is(n)=isprime(30*n+23) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A132235(n) - 23)/30 = Floor[A132235(n)/30]. - Chandler

Edited by Ray Chandler, Apr 07 2009

A158850 Numbers n such that 30*n + 29 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 7, 8, 11, 12, 13, 14, 15, 16, 18, 19, 21, 23, 26, 27, 30, 33, 34, 36, 40, 41, 42, 43, 46, 47, 49, 51, 53, 56, 62, 64, 65, 67, 68, 69, 70, 76, 77, 79, 81, 84, 85, 86, 89, 90, 92, 93, 95, 96, 97, 98, 99, 102, 103, 106, 109, 110, 111, 112, 114, 117, 121, 123, 125

Offset: 1

Ki Punches, Mar 28 2009

nonn

Encoded primes with LSD 9 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 from the quotient is in the sequence, the number is prime.

			Example: 3209 with LSD 9 and (SOD-1)/3 non-integer; Then 3209/30 = 106.966, or 106, which is in the sequence, thus 3209 is prime.

Cf. A111175, A158573, A158614, A158648, A158746, A158791, A158806.

is(n)=isprime(30*n+29) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A132236(n) - 29)/30 = Floor[A132236(n)/30]. - Chandler

Edited by Ray Chandler, Apr 07 2009

A089161 Numbers k such that 30k + 17 and 30k + 19 are twin primes.

Original entry on oeis.org

0, 3, 4, 6, 7, 11, 20, 27, 28, 42, 47, 49, 53, 55, 56, 59, 62, 66, 67, 69, 74, 75, 88, 89, 105, 108, 115, 117, 118, 125, 130, 137, 138, 140, 144, 150, 151, 154, 159, 165, 180, 182, 188, 195, 206, 227, 231, 237, 243, 248, 249, 251, 258, 262, 269, 279, 284, 286, 287

Offset: 1

Pierre CAMI, Dec 06 2003

			3 is a term since 30*3 + 17 = 107, 30 * 3 + 19 = 109, and (107, 109) are twin primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A158648 and A158806.

Cf. A001097 (twin primes).

a:=proc(n) if isprime(30*n+17)=true and isprime(30*n+19)=true then n else fi end: seq(a(n),n=0..400); # Emeric Deutsch, Jun 13 2005

Select[Range[0, 300], And @@ PrimeQ[30# + {17, 19}] &] (* Amiram Eldar, Jan 27 2020 *)

More terms from Emeric Deutsch, Jun 13 2005

cp's OEIS Frontend

A039949 Primes of the form 30n - 13.

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A111175 Numbers n such that 30*n + 1 is prime.

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A158806 Numbers n such that 30*n + 19 is prime.

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A158573 Numbers k such that 30*k + 7 is prime.

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A158614 Numbers n such that 30*n + 11 is prime.

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A158746 Numbers n such that 30*n + 13 is prime.

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A158791 Numbers n such that 30*n + 23 is prime.

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A089161 Numbers k such that 30k + 17 and 30k + 19 are twin primes.