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

1,3

Comments

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.

Links

Table of n, a(n) for n=1..63.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A066847 A370121 A057887 * A215914 A006049 A084541

Adjacent sequences: A202113 A202114 A202115 * A202117 A202118 A202119

Keyword

nonn,easy

Author

J. W. Helkenberg, Dec 11 2011

Status

approved