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Search: id:A078624
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| A078624 |
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Primes of the form 7x^3 + 5x^2 + 3x + 2. |
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+0
1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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
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PROGRAM
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(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" "); ); ) }
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CROSSREFS
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Cf. A003627, A007528.
Sequence in context: A002814 A122207 A003819 this_sequence A163319 A112969 A077452
Adjacent sequences: A078621 A078622 A078623 this_sequence A078625 A078626 A078627
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 11 2002, Jan 31 2009
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 31 2009
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