1,1

More generally, we may define "primenomial primes", primes generated by polynomials of degree n with sequentially decreasing prime coefficients: Seq(m, n) = prime(n+1)*x^n + prime(n)*x^(n-1) + ... + prime(1) for x=1..m. Here n is the degree of the polynomial, m is the range and prime(i) is the i-th prime number.

This is for n = 3 or 7*x^3 + 5*x^2 + 3*x + 2.

Seq(m,1) gives primes of the form 3n+2: see A003627, A007528.

All terms except the first are == 5 mod 12. - Zak Seidov, Feb 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Select[Table[7*n^3+5*n^2+3*n+2, {n, 0, 700}], PrimeQ] (* Vincenzo Librandi, Jul 15 2012 *)

(PARI) prnomial(n, m) = { ct=0; sr=0; p=0; d=0; d1=0; for(x=0, n, y=2; for(j=2, m+1, p = prime(j); y+=x^( j-1)*p; ); if(isprime(y), ct+=1; print1(y" "); ); ) }

(Magma) [a: n in [0..500] | IsPrime(a) where a is 7*n^3+5*n^2+ 3*n+2 ]; // Vincenzo Librandi, Jul 15 2012

Cf. A003627, A007528.

Sequence in context: A122207 A174305 A003819 * A163319 A269836 A114950

Adjacent sequences: A078621 A078622 A078623 * A078625 A078626 A078627

easy,nonn

Cino Hilliard, Dec 11 2002, Jan 31 2009

Edited by N. J. A. Sloane, Jan 31 2009

approved