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A217722 Primes one less than the sum of the square of a prime and the cube of a prime. 0
11, 149, 173, 293, 367, 463, 631, 653, 1303, 1451, 1493, 1499, 1619, 1973, 2221, 2333, 2551, 2557, 2699, 3011, 3037, 3539, 3823, 3877, 4139, 4831, 4937, 5051, 5081, 5273, 5441, 6659, 6761, 6883, 6907, 7013, 7027, 7121, 7219, 7237, 7699, 8219, 8263, 8539, 8707 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A number p is a term of this sequence iff p = q^2 + r^3 - 1 where p, q and r are all prime.
There are 1064 such numbers < 10^7.
LINKS
EXAMPLE
173 is in the sequence because 173 = 7^2 + 5^3 - 1, and 173, 7, and 5 are all prime.
MATHEMATICA
max = 10^4; Take[Select[Sort[Flatten[Table[Prime[p]^2 + Prime[q]^3 - 1, {p, PrimePi[Sqrt[max]]}, {q, PrimePi[max^(1/3)]}]]], PrimeQ[#] && # < max &] (* Alonso del Arte, Mar 22 2013 *)
CROSSREFS
This sequence contains the prime numbers from A045699-1;
primes of the form p1^2 + p2^3: A045700;
primes of the form p1^2 + p2^3 + 1: A217734.
Sequence in context: A194726 A367790 A296143 * A261536 A175635 A103544
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 28 07:05 EST 2024. Contains 370387 sequences. (Running on oeis4.)