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

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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..62.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A039097 A047581 A039067 * A228090 A287440 A111175

Adjacent sequences: A202111 A202112 A202113 * A202115 A202116 A202117

Keyword

nonn,easy

Author

J. W. Helkenberg, Dec 11 2011

Status

approved