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

71, 281, 491, 701, 2801, 4481, 7001, 7841, 12251, 13721, 17921, 28001, 34301, 54881, 70001, 78401, 85751, 122501, 125441, 137201, 168071, 240101, 280001, 286721, 437501, 490001

Offset: 1

Author

Jonathan Vos Post, Feb 22 2006

Keywords

• nonn

Comments

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.

Examples

			a(1) = 71 = 2^1 * 5^1 * 7^1 + 1.
a(2) = 281 = 2^3 * 5^1 * 7^1 + 1.
a(3) = 491 = 2^1 * 5^1 * 7^2 + 1.
a(4) = 701 = 2^2 * 5^2 * 7^1 + 1.
a(5) = 2801 = 2^4 * 5^2 * 7^1 + 1.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A005109, A030430.

Programs

Mathematica

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 *)

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(tCharles R Greathouse IV, Feb 17 2011

Extensions

Corrected by T. D. Noe, Nov 15 2006