A181732 -id:A181732 - cp's OEIS frontend

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

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

A224889 Numbers n such that 90n + 91 is prime.

Original entry on oeis.org

1, 2, 5, 6, 8, 10, 12, 16, 17, 19, 23, 24, 25, 27, 30, 32, 33, 36, 38, 40, 44, 46, 50, 53, 54, 61, 64, 67, 68, 69, 71, 72, 73, 75, 83, 85, 88, 89, 90, 93, 95, 96, 97, 99, 100, 101, 106, 107, 108, 109, 116, 118, 120, 122, 123, 124, 129, 132, 135, 137, 138, 139

Offset: 1

J. W. Helkenberg, Jul 24 2013

Equals A181732 - 1.

Michael B. Porter, Table of n, a(n) for n = 1..10000

Mathematica
```
Select[Range[0, 400], PrimeQ[90# +91]&]
```

isA224889(n) = isprime(90*n + 91) \\ Michael B. Porter, Jul 28 2013

A255491 Numbers k such that 90*k+1 is composite.

Original entry on oeis.org

1, 4, 5, 8, 10, 12, 14, 15, 16, 19, 21, 22, 23, 27, 29, 30, 32, 35, 36, 38, 40, 42, 43, 44, 46, 48, 49, 50, 52, 53, 56, 57, 58, 59, 60, 61, 63, 64, 66, 67, 71, 75, 77, 78, 79, 80, 81, 82, 83, 85, 87, 88, 92, 93, 95, 99, 103, 104, 105, 106

Offset: 1

N. J. A. Sloane, Mar 03 2015

nonn

J. W. Helkenberg, Email message, Mar 02 2015.

Vincenzo Librandi, Table of n, a(n) for n = 1..7000

Complement of A181732.

[n: n in [1..120]| not IsPrime(90*n+1)]; // Vincenzo Librandi, Jun 09 2017

Select[Range[200], !PrimeQ[90 # + 1] &] (* Vincenzo Librandi, Jun 09 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

A224865 Numbers n such that 90n + 89 and 90n + 91 are twin primes.

Original entry on oeis.org

1, 2, 8, 17, 25, 30, 32, 36, 44, 46, 64, 69, 72, 73, 83, 88, 97, 99, 106, 107, 116, 118, 120, 122, 123, 129, 132, 135, 151, 184, 186, 190, 198, 205, 211, 220, 233, 239, 253, 255, 262, 282, 296, 305, 314, 317, 331, 342, 347, 352, 365, 374, 382, 384, 391, 396, 409

Offset: 1

J. W. Helkenberg, Jul 22 2013

nonn

Cf. A202116, A181732, A224889.

A202116 INTERSECT A181732+1; A202116 INTERSECT A224889

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

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A224889 Numbers n such that 90n + 91 is prime.

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A255491 Numbers k such that 90*k+1 is composite.

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

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A224865 Numbers n such that 90*n + 89 and 90*n + 91 are twin primes.

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A224865 Numbers n such that 90n + 89 and 90n + 91 are twin primes.