A078625 Primes of the form 2*x^3 + 3*x^2 + 5*x + 7.

7, 17, 103, 577, 1753, 2357, 4973, 7507, 56857, 62627, 97387, 273367, 342107, 588397, 895667, 967753, 1005203, 1250357, 1635133, 1688153, 2554963, 3002653, 3328433, 3587657, 4976107, 5087087, 6550043, 6818257, 7234153, 10627753, 13827257, 15881003, 17105203

Offset

1,1

Comments

Original name: Primenomial primes: primes generated by polynomials of degree n with sequentially increasing prime coefficients. This is for n = 3 or 2x^3 + 3x^2 + 5x + 7.

Unlike the sequence for descending prime coefficients, this sequence allows n to be even also.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

Seq(m, n) = prime(1)x^n + prime(2)x^(n-1) + ... prime(n+1) for x=1..m. n is the degree of the polynomial, m is the range and prime(i) is the i-th prime number. If Seq(m, n) is prime, list it.

Maple

f:= x-> (p-> `if`(isprime(p), p, [][]))(7+(5+(3+2*x)*x)*x):
map(f, [$0..250])[];  # Alois P. Heinz, Jul 07 2025

Prog

(PARI) prnomial2(n, m) = { ct=0; sr=0; p=0; d=0; d1=0; for(x=0, n, y=prime(m+1); for(j=1, m, p = prime(j); y+=x^(m+1-j)*p; ); if(isprime(y), ct+=1; print1(y" "); ); ) }

Crossrefs

Cf. A003627, A007528.

Sequence in context: A092057 A395799 A082738 * A092340 A181605 A284209

Adjacent sequences: A078622 A078623 A078624 * A078626 A078627 A078628

Keyword

easy,nonn

Author

Cino Hilliard, Dec 11 2002

Extensions

a(1)=7 inserted by Sean A. Irvine, Jul 07 2025

Status

approved