A201804 -id:A201804 - cp's OEIS frontend

A201816 Numbers k such that 90*k + 13 is prime.

0, 1, 2, 3, 4, 5, 7, 8, 9, 12, 16, 17, 19, 22, 23, 30, 31, 35, 36, 37, 38, 40, 42, 46, 47, 49, 50, 51, 53, 58, 59, 60, 61, 63, 66, 67, 68, 74, 75, 80, 82, 84, 86, 88, 92, 95, 99, 100, 101, 103, 105, 107, 108, 112, 114, 116, 119, 121, 122, 123, 124, 126, 127

Offset: 1

J. W. Helkenberg, Dec 05 2011

Looking at the format 90*k+13 modulo 9 and modulo 10 we see that all entries of A142318 have digital root 4 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804.

[n: n in [0..200] | IsPrime(90*n+13)]; // Vincenzo Librandi, Dec 12 2011

a:= proc(n) option remember; local k;
       for k from 1+ `if`(n=1, -1, a(n-1))
       while not isprime(90*k+13) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 06 2011

Select[Range[0,4000],PrimeQ[90 #+13]&] (* Vincenzo Librandi, Dec 12 2011 *)

is(n)=isprime(90*n+13) \\ Charles R Greathouse IV, Jul 12 2016

A201817 Numbers k such that 90*k + 67 is prime.

Original entry on oeis.org

0, 1, 3, 6, 8, 9, 10, 13, 14, 17, 19, 20, 23, 29, 30, 31, 33, 35, 36, 42, 44, 47, 50, 51, 56, 57, 61, 62, 63, 64, 66, 69, 70, 72, 73, 76, 77, 79, 83, 85, 90, 94, 96, 98, 100, 101, 103, 107, 108, 110, 117, 118, 120, 121, 122, 125, 127, 128, 129, 133, 138, 139

Offset: 1

J. W. Helkenberg, Dec 05 2011

Looking at the format 90*k + 67 modulo 9 and modulo 10 we see that all entries of A142323 have digital root 4 and last digit 7. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816.

[n: n in [0..200] | IsPrime(90*n+67)]; // Vincenzo Librandi, Dec 12 2011

a:= proc(n) option remember; local k;
       for k from 1+ `if`(n=1, -1, a(n-1))
       while not isprime(90*k+67) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 06 2011

Select[Range[0,4000],PrimeQ[90 #+67]&] (* Vincenzo Librandi, Dec 12 2011 *)

is(n)=isprime(90*n+67) \\ Charles R Greathouse IV, Feb 17 2017

A201820 Numbers k such that 90*k + 23 is prime.

Original entry on oeis.org

0, 1, 3, 4, 6, 7, 8, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 25, 28, 29, 32, 34, 39, 40, 42, 45, 47, 50, 52, 53, 55, 57, 59, 63, 64, 67, 68, 70, 76, 78, 84, 85, 87, 90, 95, 96, 97, 99, 102, 103, 105, 108, 109, 110, 112, 113, 116, 119, 122, 123, 125, 129, 131

Offset: 1

J. W. Helkenberg, Dec 05 2011

This sequence was generated by adding 12 Fibonacci-like sequences. Looking at the format 90*k+23 modulo 9 and modulo 10 we see that all entries of A142324 have digital root 5 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818.

[n: n in [0..200] | IsPrime(90*n+23)]; // Vincenzo Librandi, Dec 11 2011

Select[Range[0,400],PrimeQ[90 #+23]&] (* Vincenzo Librandi, Dec 11 2011 *)

is(n)=isprime(90*n+23) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A142324(n) - 23)/90.

A201822 Numbers k such that 90*k + 77 is prime.

Original entry on oeis.org

1, 2, 3, 6, 8, 9, 10, 15, 17, 18, 19, 20, 24, 26, 29, 30, 32, 34, 37, 40, 41, 43, 45, 46, 48, 54, 58, 59, 60, 62, 65, 68, 69, 74, 75, 76, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 102, 104, 109, 111, 113, 114, 115, 117, 122, 128, 130, 131, 135, 138, 144

Offset: 1

J. W. Helkenberg, Dec 05 2011

Looking at the format 90k+77 modulo 9 and modulo 10 we see that all entries of A142329 have digital root 5 and last digit 7. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820.

[n: n in [0..200] | IsPrime(90*n+77)]; // Vincenzo Librandi, Dec 11 2011

Select[Range[0,400],PrimeQ[90 #+77]&] (* Vincenzo Librandi, Dec 11 2011 *)

is(n)=isprime(90*n+77) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A142329(n) - 77)/90.

A202101 Numbers k such that 90*k + 59 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 11, 13, 14, 15, 16, 21, 22, 23, 25, 26, 28, 32, 34, 35, 36, 37, 40, 43, 44, 47, 51, 54, 55, 56, 57, 58, 62, 67, 69, 70, 71, 74, 76, 78, 81, 83, 89, 93, 95, 96, 99, 100, 102, 104, 107, 112, 116, 117, 120, 121, 126, 127, 128, 132, 134, 138

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 12 Fibonacci-like sequences [see: PROG]. Looking at 90*n+59 modulo 9 and modulo 10 we see that all entries of A142319 have digital root 5 and last digit 9. (Reverting the process is an application of the Chinese remainder theorem)

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822.

Select[Range[0, 200], PrimeQ[90 # + 59] &]

is(n)=isprime(90*n+59) \\ Charles R Greathouse IV, Feb 17 2017

A202104 Numbers k such that 90*k + 41 is prime.

Original entry on oeis.org

0, 1, 3, 4, 5, 8, 10, 11, 14, 16, 17, 21, 23, 26, 30, 33, 35, 37, 38, 42, 43, 44, 45, 47, 49, 52, 56, 57, 58, 59, 60, 61, 63, 64, 66, 72, 74, 75, 77, 79, 81, 85, 91, 94, 96, 98, 99, 100, 102, 103, 105, 109, 110, 113, 114, 115, 127, 131, 133, 134, 136, 140

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 12 Fibonacci-like sequences [See: PROG]. Looking at the format 90k+41 modulo 9 and modulo 10 we see that all entries of A142333 have digital root 5 and last digit 1. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the PERL program) from the base pairs 49*91, 19*59, 37*23, 73*77, 11*61, 29*79, 47*43, 83*7, 13*17, 31*71, 49*89, 67*53.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101.

Select[Range[0, 200], PrimeQ[90 # + 41] &]

is(n)=isprime(90*n+41) \\ Charles R Greathouse IV, Feb 17 2017

A202105 Numbers k such that 90*k + 43 is prime.

Original entry on oeis.org

0, 2, 3, 7, 9, 11, 12, 13, 14, 16, 18, 19, 21, 23, 24, 25, 26, 27, 31, 37, 38, 40, 41, 42, 44, 45, 47, 48, 52, 53, 54, 55, 60, 62, 67, 68, 70, 74, 75, 76, 80, 81, 84, 87, 88, 89, 91, 98, 100, 101, 104, 114, 118, 119, 123, 126, 130, 131, 132, 137, 139, 142

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 12 Fibonacci-like sequences [See: PROG]. Looking at the format 90k+43 modulo 9 and modulo 10 we see that all entries of A142334 have digital root 7 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q values given in the PERL program) from the base p,q pairs 43*91, 19*7, 37*79, 73*61, 11*53, 29*17, 47*89, 83*71, 13*31, 49*67, 23*41, 59*77.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104.

Select[Range[0, 200], PrimeQ[90 # + 43] &]

is(n)=isprime(90*n+43) \\ Charles R Greathouse IV, Feb 17 2017

A202110 Numbers n such that 90*n + 7 is prime.

Original entry on oeis.org

0, 1, 3, 4, 5, 6, 8, 10, 11, 12, 16, 18, 22, 26, 27, 29, 30, 31, 32, 34, 39, 40, 41, 43, 44, 45, 48, 50, 51, 55, 58, 60, 65, 67, 69, 71, 73, 78, 80, 81, 83, 88, 89, 92, 93, 94, 96, 97, 100, 102, 103, 106, 109, 110, 113, 114, 115, 118, 122, 125, 127, 128, 129

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 12 Fibonacci-like sequences [See: PROG]. Looking at the format 90n+7 modulo 9 and modulo 10 we see that all entries of A142315 have digital root 7 and last digit 7. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q values given in the PERL program) from the base p,q pairs 7*91, 19*43, 37*61, 73*79, 11*17, 29*53, 47*71, 83*89, 13*49, 31*67, 23*59, 41*77.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105.

Select[Range[0, 200], PrimeQ[90 # + 7] &]

is(n)=isprime(90*n+7) \\ Charles R Greathouse IV, Feb 17 2017

A202112 Numbers n such that 90n + 79 is prime.

Original entry on oeis.org

0, 3, 4, 6, 7, 11, 13, 15, 17, 18, 19, 20, 24, 29, 33, 35, 36, 38, 41, 45, 46, 52, 56, 57, 60, 61, 62, 63, 64, 68, 70, 71, 75, 81, 82, 83, 84, 89, 90, 91, 94, 95, 96, 103, 104, 106, 111, 112, 115, 119, 122, 123, 124, 125, 129, 130, 132, 133, 137, 139, 146

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 14 Fibonacci-like sequences [See: PROG]. Looking at the format 90n+79 modulo 9 and modulo 10 we see that all entries of A142330 have digital root 7 and last digit 9. (Reverting the process is an application of the Chinese remainder theorem.) The 14 Fibonacci-like sequences are generated (via the p and q values given in the PERL program) from the base p,q pairs 79*91, 19*61, 37*7, 73*43, 11*89, 29*71, 47*17, 83*53, 13*13, 31*49, 67*67, 23*23, 41*59, 77*77.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110.

Select[Range[0, 200], PrimeQ[90 # + 79] &]

is(n)=n%90==79 && isprime(n) \\ Charles R Greathouse IV, Jun 01 2016

a(n) ~ 24n log n. - Charles R Greathouse IV, Jun 01 2016

A202113 Numbers n such that 90n + 61 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 11, 13, 14, 20, 21, 23, 24, 25, 29, 31, 34, 36, 37, 39, 43, 44, 45, 46, 50, 51, 53, 55, 56, 58, 62, 64, 67, 69, 70, 71, 77, 81, 84, 90, 93, 94, 99, 101, 102, 104, 105, 106, 108, 109, 112, 114, 116, 119, 120, 123, 125, 127, 132, 135, 136

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 14 Fibonacci-like sequences [See: PROG]. Looking at the format 90n+61 modulo 9 and modulo 10 we see that all entries of A142330 have digital root 7 and last digit 1. (Reverting the process is an application of the Chinese remainder theorem.) The 14 Fibonacci-like sequences are generated (via the p and q values given in the Perl program) from the base p,q pairs 61*91, 19*79, 37*43, 73*7, 11*71, 29*89, 47*53, 83*17, 13*67, 31*31, 49*49, 23*77, 41*41, 59*59.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112.

Select[Range[0, 200], PrimeQ[90 # + 61] &]

is(n)=isprime(90*n+61) \\ Charles R Greathouse IV, Feb 17 2017

cp's OEIS Frontend

A201816 Numbers k such that 90*k + 13 is prime.

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A201817 Numbers k such that 90*k + 67 is prime.

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A201820 Numbers k such that 90*k + 23 is prime.

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A201822 Numbers k such that 90*k + 77 is prime.

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A202101 Numbers k such that 90*k + 59 is prime.

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A202104 Numbers k such that 90*k + 41 is prime.

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A202105 Numbers k such that 90*k + 43 is prime.

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A202110 Numbers n such that 90*n + 7 is prime.

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