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A176914 Smarandache friendly prime pairs (SFPP) 1
2, 5, 3, 13, 5, 31, 7, 53, 3536123, 128541727 (list; graph; refs; listen; history; text; internal format)



Given any sequence a1, a2, ..., two elements of the sequence, a_m and a_n, are called a Smarandache Friendly Pair (SFP) with respect to the sequence if (a_m)x(a_n) = a_m + a_(m+1) + ... + a_n. When the sequence is the prime numbers one gets a SFPP. First four SFPPs were found by F. Russo and the fifth one by Philip Gibbs. It is not known whether other SFPPs exist, or if there are finitely or infinitely many.


Philip Gibbs, "A Fifth Smarandache Friendly Prime Pair", http://vixra.org/abs/1004.0126

A. Murphy, "Smarandache friendly numbers and a few more sequences", Smarandache Notions Journal, Vol. 12, 1-2-3, Spring 2001.

Felice Russo, "On a problem concerning the Smarandache friendly prime pairs", Smarandache Notions Journal, pp. 56-58, 2002


Table of n, a(n) for n=1..10.

Philip Gibbs, A Fifth Smarandache Friendly Prime Pair

Felice Russo, On a problem concerning the Smarandache friendly prime pairs

Digital Library of Sciences


(2, 5) is a SFPP because 2 and 5 are primes, and 2x5 = 2 + 3 + 5. Similarly (3, 13) is a SFPP because 3 and 13 are primes, and 3x13 = 3 + 5 + 7 + 11 + 13.


Sequence in context: A120858 A124937 A169852 * A194010 A229609 A242171

Adjacent sequences:  A176911 A176912 A176913 * A176915 A176916 A176917




G. Ornea (gornea2005(AT)gmail.com), Apr 28 2010



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Last modified December 4 15:24 EST 2016. Contains 278750 sequences.