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A114992 Primes of the form 2^a * 5^b * 7^c + 1 for positive a, b, c.

%I A114992 #19 Sep 10 2024 20:46:53
%S A114992 71,281,491,701,2801,4481,7001,7841,12251,13721,17921,28001,34301,
%T A114992 54881,70001,78401,85751,122501,125441,137201,168071,240101,280001,
%U A114992 286721,437501,490001
%N A114992 Primes of the form 2^a * 5^b * 7^c + 1 for positive a, b, c.
%C A114992 Since the factors of 2 and 5 are the same as a factor of 10, a subset of A030430 "primes of form 10n+1." There are subsequences such as 71, 701, 7001, 70001, 700001, 700000001, 7000000001; 281, 2801, 280001, 2800001; 491, 490001, 4900001, 490000001, 49000000001, 490000000001.
%H A114992 Charles R Greathouse IV, <a href="/A114992/b114992.txt">Table of n, a(n) for n = 1..10000</a>
%e A114992 a(1) = 71 = 2^1 * 5^1 * 7^1 + 1.
%e A114992 a(2) = 281 = 2^3 * 5^1 * 7^1 + 1.
%e A114992 a(3) = 491 = 2^1 * 5^1 * 7^2 + 1.
%e A114992 a(4) = 701 = 2^2 * 5^2 * 7^1 + 1.
%e A114992 a(5) = 2801 = 2^4 * 5^2 * 7^1 + 1.
%t A114992 With[{nn=30},Take[Select[Union[2^#[[1]]*5^#[[2]]*7^#[[3]]+1&/@Tuples[ Range[nn],3]],PrimeQ],nn]] (* _Harvey P. Dale_, Aug 24 2012 *)
%o A114992 (PARI) find(lim)=my(v=List(), t); for(b=1,log(lim\14)\log(5), for(c=1,log(lim\2\5^b)/log(7), t=2*5^b*7^c; while(t<lim, if(ispseudoprime(t+1), listput(v,t+1)); t+=t))); vecsort(Vec(v));
%o A114992 find(10^100) \\ _Charles R Greathouse IV_, Feb 17 2011
%Y A114992 Cf. A000040, A005109, A030430.
%K A114992 nonn
%O A114992 1,1
%A A114992 _Jonathan Vos Post_, Feb 22 2006
%E A114992 Corrected by _T. D. Noe_, Nov 15 2006