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A114992 Primes of the form 2^a * 5^b * 7^c + 1 for positive a, b, c. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A141943 A167441 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

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Last modified May 7 00:22 EDT 2021. Contains 343609 sequences. (Running on oeis4.)