A158573 -id:A158573 - cp's OEIS frontend

A132231 Primes congruent to 7 (mod 30).

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

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

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

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

A332772 Numbers k > 0 such that 30k +- 7 is prime.

Original entry on oeis.org

1, 2, 3, 4, 9, 10, 12, 13, 15, 19, 20, 25, 26, 29, 32, 33, 37, 41, 43, 48, 52, 53, 54, 58, 66, 67, 76, 78, 81, 85, 88, 89, 90, 92, 95, 97, 101, 107, 118, 120, 121, 128, 129, 134, 143, 150, 153, 155, 165, 166, 172, 178, 180, 194, 195, 202, 207, 209, 211, 212

Offset: 1

Frank Ellermann, Feb 25 2020

Looking for prime factors > 5=prime(3) in 8=A005867(3) candidates mod 30=A002110(3) two candidates in the form 30k +- 7 with k > 0 never belong to a twin prime pair. Twin primes can be (30k-13, 30k-11) A331840, (30k-1, 30k +1) A176114, or (30k+11, 30k+13) A089160.

			a(4)=4 for prime(30)=113=4*30-7 and prime(31)=127=4*30+7.
a(5)=9 for prime(56)=263=9*30-7 and prime(59)=277=9*30+7.

Frank Ellermann, Illustration for A002110, A005867, A038110, A060753

Cf. A000040, A002110, A005867, A089160, A176114, A331840.

Subsequence of A158573. Prime pairs 30k +- 7 in A329262.

Select[Range@ 215, AllTrue[30 # + {-7, 7}, PrimeQ] &] (* Michael De Vlieger, Feb 25 2020 *)

S = 1
do N = 2 while length( S ) < 255
   if NOPRIME( N * 30 + 7 )   then  iterate N
   if NOPRIME( N * 30 - 7 )   then  iterate N
   S = S || ',' N
end N
say S

cp's OEIS Frontend

A132231 Primes congruent to 7 (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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A158614 Numbers n such that 30*n + 11 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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