A201816 -id:A201816 - cp's OEIS frontend

A201819 Numbers n such that 90*n + 31 is prime.

0, 2, 6, 7, 8, 11, 13, 14, 15, 16, 19, 20, 22, 25, 26, 28, 30, 33, 35, 36, 37, 39, 40, 47, 49, 51, 53, 60, 61, 63, 64, 65, 68, 71, 74, 75, 76, 77, 81, 82, 84, 85, 88, 91, 92, 95, 97, 99, 104, 107, 110, 112, 118, 120, 128, 130, 131, 138, 139, 141, 146, 149

Offset: 1

J. W. Helkenberg, Dec 05 2011

This sequence was generated by adding 14 Fibonacci-like sequences. Looking at the format 90n+31 modulo 9 and modulo 10 we see that all entries of A142328 have digital root 4 and last digit 1. (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, A201818.

[n: n in [0..200] | IsPrime(90*n+31)] // Vincenzo Librandi, Dec 11 2011

Select[Range[0, 200], PrimeQ[90 # + 31] &] (* T. D. Noe, Dec 06 2011 *)

is(n)=isprime(90*n+31) \\ Charles R Greathouse IV, Feb 20 2017

A202114 Numbers n such that 90n + 53 is prime.

Original entry on oeis.org

0, 2, 5, 6, 7, 8, 9, 10, 13, 16, 17, 24, 26, 29, 30, 31, 33, 35, 42, 43, 44, 47, 48, 49, 51, 52, 55, 58, 64, 65, 68, 69, 70, 75, 77, 80, 82, 83, 85, 86, 87, 91, 93, 94, 96, 97, 99, 103, 104, 112, 113, 114, 120, 124, 126, 127, 132, 134, 135, 138, 140, 141

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+53 modulo 9 and modulo 10 we see that all entries of A142316 have digital root 8 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 "seed" values entered into the PERL program) from the base p,q pairs 53*91, 19*17, 37*89, 73*71, 11*13, 29*67, 47*49, 83*31, 23*61, 41*43, 59*7, 77*79.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112, A202113.

Select[Range[0, 200], PrimeQ[90 # + 53] &]

is(n)=isprime(90*n+53) \\ Charles R Greathouse IV, Feb 20 2017

A202116 Numbers n such that 90n + 89 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 13, 15, 17, 18, 20, 21, 22, 25, 28, 29, 30, 31, 32, 36, 41, 44, 45, 46, 48, 51, 55, 58, 59, 62, 64, 65, 66, 69, 70, 72, 73, 77, 78, 83, 84, 86, 87, 88, 92, 97, 99, 105, 106, 107, 111, 112, 113, 116, 118, 119, 120, 121, 122, 123, 127, 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+89 modulo 9 and modulo 10 we see that all entries of A142335 have digital root 8 and last digit 9. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q "seed" values entered into the PERL program) from the base p,q pairs 89*91, 19*71, 37*17, 73*53, 11*49, 29*31, 47*67, 83*13, 23*43, 41*79, 59*61, 77*7.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112, A202113, A202114, A202115.

Select[Range[0, 200], PrimeQ[90 # + 89] &]

is(n)=isprime(90*n+89) \\ Charles R Greathouse IV, Jun 06 2017

A202129 Numbers n such that 90n + 71 is prime.

Original entry on oeis.org

0, 2, 4, 5, 7, 9, 10, 11, 12, 16, 17, 20, 23, 26, 28, 31, 33, 35, 38, 39, 40, 41, 42, 46, 48, 49, 52, 54, 55, 59, 60, 62, 63, 66, 67, 72, 76, 77, 82, 83, 87, 89, 90, 101, 103, 104, 105, 108, 111, 112, 114, 117, 118, 119, 125, 126, 129, 133, 137, 138, 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 90n+71 modulo 9 and modulo 10 we see that all entries of A142325 have digital root 8 and last digit 1. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q "seed" values entered into the Perl program) from the base p,q pairs 71*91, 19*89, 37*53, 73*13, 11*31, 29*49, 47*13, 83*67, 23*7, 41*61, 59*79, 77*43.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112, A202113, A202114, A202115, A202116.

Select[Range[0, 200], PrimeQ[90 # + 71] &]

is(n)=isprime(90*n+71) \\ Charles R Greathouse IV, Jun 13 2017

A224854 Numbers n such that 90n + 11 and 90n + 13 are twin prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 9, 12, 16, 19, 23, 30, 31, 36, 47, 49, 58, 61, 68, 75, 80, 92, 100, 103, 105, 112, 114, 124, 126, 134, 135, 136, 140, 152, 159, 162, 173, 192, 199, 210, 213, 217, 222, 227, 233, 239, 240, 255, 278, 281, 288, 290, 303, 313, 346, 350, 357

Offset: 1

J. W. Helkenberg, Jul 22 2013

All matching entries for A201804 and A201816 are twin prime numbers.

Cf. A201804, A201816.

Select[Range[0, 499], PrimeQ[90# + 11] && PrimeQ[90# + 13] &]

Missing terms added from Bruno Berselli, Jul 23 2013

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A201819 Numbers n such that 90*n + 31 is prime.

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A202114 Numbers n such that 90n + 53 is prime.

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A202116 Numbers n such that 90n + 89 is prime.

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A202129 Numbers n such that 90n + 71 is prime.

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A224854 Numbers n such that 90*n + 11 and 90*n + 13 are twin prime.

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A224854 Numbers n such that 90n + 11 and 90n + 13 are twin prime.