A001259 - OEIS

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)

3, 5, 7, 17, 19, 37, 97, 113, 257, 401, 487, 631, 971, 1297, 1801, 19457, 22051, 28817, 65537, 157303, 160001

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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

Table of n, a(n) for n=1..21.

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

Cf. A007015, A342701.

Sequence in context: A169628 A171254 A092951 * A248370 A087126 A348438

Adjacent sequences: A001256 A001257 A001258 * A001260 A001261 A001262

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane

EXTENSIONS

New name, giving a definition, by Jonathan Sondow, Oct 06 2012

STATUS

approved