A158614 -id:A158614 - cp's OEIS frontend

A132232 Primes congruent to 11 (mod 30).

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

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

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

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

cp's OEIS Frontend

A132232 Primes congruent to 11 (mod 30).

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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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A158648 Numbers n such that 30*n + 17 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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