A202110 Numbers n such that 90*n + 7 is prime.

0, 1, 3, 4, 5, 6, 8, 10, 11, 12, 16, 18, 22, 26, 27, 29, 30, 31, 32, 34, 39, 40, 41, 43, 44, 45, 48, 50, 51, 55, 58, 60, 65, 67, 69, 71, 73, 78, 80, 81, 83, 88, 89, 92, 93, 94, 96, 97, 100, 102, 103, 106, 109, 110, 113, 114, 115, 118, 122, 125, 127, 128, 129

Offset: 1

Author

J. W. Helkenberg, Dec 11 2011

Keywords

• nonn
• easy

Comments

This sequence was generated by adding 12 Fibonacci-like sequences [See: PROG]. Looking at the format 90n+7 modulo 9 and modulo 10 we see that all entries of A142315 have digital root 7 and last digit 7. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q values given in the PERL program) from the base p,q pairs 7*91, 19*43, 37*61, 73*79, 11*17, 29*53, 47*71, 83*89, 13*49, 31*67, 23*59, 41*77.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 200], PrimeQ[90 # + 7] &]

PARI

is(n)=isprime(90*n+7) \\ Charles R Greathouse IV, Feb 17 2017