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A001259
A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is a prime factor of twice the product.
(Formerly M2423 N0958)
5
3, 5, 7, 17, 19, 37, 97, 113, 257, 401, 487, 631, 971, 1297, 1801, 19457, 22051, 28817, 65537, 157303, 160001
OFFSET
1,1
COMMENTS
Old name was: A special sequence of primes.
Holt shows this sequence is complete. - T. D. Noe, Jul 28 2005
This sequence was used by Schinzel (1958) and Schinzel and Wakulicz (1959) to prove that there are at least two solutions k to phi(n+k) = phi(k) for all n <= 8*10^47 and 2*10^58, respectively. - Amiram Eldar, Mar 19 2021
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Jeffery J. Holt, The minimal number of solutions to phi(n)=phi(n+k), Math. Comp., 72 (2003), 2059-2061.
A. Schinzel and Andrzej Wakulicz, Sur l'équation phi(x+k)=phi(x), I., Acta Arith. 4 (1958), 181-184. - Jonathan Sondow, Oct 07 2012
A. Schinzel and Andrzej Wakulicz; Sur l'équation phi(x+k)=phi(x). II. Acta Arith. 5 1959 425-426.
CROSSREFS
Sequence in context: A169628 A171254 A092951 * A248370 A087126 A348438
KEYWORD
nonn,fini,full
EXTENSIONS
New name, giving a definition, by Jonathan Sondow, Oct 06 2012
STATUS
approved