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

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

Author

J. W. Helkenberg, Dec 11 2011

Keywords

• nonn
• easy

Comments

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.

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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