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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)
OFFSET

1,1

COMMENTS

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.

REFERENCES

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

LINKS

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

EXAMPLE

(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.

CROSSREFS

Sequence in context: A120858 A124937 A169852 * A194010 A229609 A091265

Adjacent sequences:  A176911 A176912 A176913 * A176915 A176916 A176917

KEYWORD

nonn,less

AUTHOR

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

STATUS

approved

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Last modified April 17 20:01 EDT 2014. Contains 240655 sequences.