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

1,1

Comments

Compare with A005109 "Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1." One might call this new sequence "(2,5,7)-Pierpont) primes."

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.

Links

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

Example

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.

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 *)

Prog

(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));
find(10^100) \\ Charles R Greathouse IV, Feb 17 2011

Crossrefs

Cf. A000040, A005109, A030430.

Sequence in context: A167441 A349084 A140856 * A158734 A126021 A142548

Adjacent sequences: A114989 A114990 A114991 * A114993 A114994 A114995

Keyword

nonn

Author

Jonathan Vos Post, Feb 22 2006

Extensions

Corrected by T. D. Noe, Nov 15 2006

Status

approved