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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 (list; graph; refs; listen; history; text; internal format)
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^(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 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^( 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

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

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)