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A243100 Primes of the form x^(y+1)-y^x, for x,y > 0. 4
3, 7, 19, 179, 543607, 129136067, 94143168179, 11920928949924493, 36472996377170722403, 61159026180004467059, 1341068619659378429383, 10301051460877537453973547005699, 710542735760100185871124061615149, 17763568394002504646778106434649157 (list; graph; refs; listen; history; text; internal format)
See A123206 for primes of the form x^y-y^x with x,y>1. If y=1 is allowed, any prime p is obtained for x=p+1; this motivates the "y+1" in the exponent of the present sequence.
See also A086877 (and A098463) for primes of the form (x+1)^x-x^x.
y=0 would give "Primes of the form x", so y>0 is required. y=1 gives x^2-1 = (x-1)*(x+1) which is only prime for x=2. - Jens Kruse Andersen, Aug 23 2014
Jens Kruse Andersen, Table of n, a(n) for n = 1..59
J. S. Gerasimov, x^(y + 1) - y^x, SeqFan list, Aug 18, 2014
(PARI) a=[]; for(S=1, 199, for(x=1, S-1, ispseudoprime(p=x^(1+y=S-x)-y^x)&&a=concat(a, p))); vecsort(a) \\ The list calculated this way is probably not complete up to the last terms. E.g., a 46 digit prime is found for x=3, y=97 after three larger terms for smaller S=x+y.
(PARI) m=300; a=[]; for(x=1, m+5, for(y=1, m+5, p=x^(y+1)-y^x; if(p<2^m && ispseudoprime(p), a=concat(a, p)))); a=vecsort(a) \\ Compute all terms below 2^m. Jens Kruse Andersen, Aug 23 2014
See also A072164.
Sequence in context: A118128 A113875 A111974 * A173400 A281971 A230352
M. F. Hasler, Aug 19 2014

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Last modified June 7 04:44 EDT 2023. Contains 363151 sequences. (Running on oeis4.)