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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.
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%I #7 Mar 09 2014 14:01:29

%S 17,103,577,1753,2357,4973,7507,56857,62627,97387,273367,342107,

%T 588397,895667,967753,1005203,1250357,1635133,1688153,2554963,3002653,

%U 3328433,3587657,4976107,5087087,6550043,6818257,7234153,10627753,13827257

%N 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.

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

%F 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.

%e Seq(100,2) = 19 157 439 1039 1229 1657 3659 5569 6907 7879 8389 10589 14369 17209 17959 19507

%o (PARI) prnomial2(n,m) = { ct=0; sr=0; p=0; d=0; d1=0; for(x=1,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" "); ); ) }

%Y Cf. A003627, A007528.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Dec 11 2002