

A078624


Primes of the form 7x^3 + 5x^2 + 3x + 2.


1



2, 17, 49877, 112577, 141509, 1312769, 3753137, 5316677, 6841397, 9635357, 31581497, 33930977, 37669277, 41672537, 45949829, 47438057, 62303069, 84325817, 93465929, 130619297, 149162009, 162450857, 172919477, 191350217
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OFFSET

1,1


COMMENTS

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^(n1) + ... prime(1) for x=1..m. Here n is the degree of the polynomial, m is the range and prime(i) is the ith prime number.
This is for n = 3 or 7x^3 + 5x^2 + 3x + 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


LINKS

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


MATHEMATICA

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


PROG

(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^( j1)*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


CROSSREFS

Cf. A003627, A007528.
Sequence in context: A122207 A174305 A003819 * A163319 A269836 A114950
Adjacent sequences: A078621 A078622 A078623 * A078625 A078626 A078627


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Dec 11 2002, Jan 31 2009


EXTENSIONS

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


STATUS

approved



