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.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

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

Cf. A007015, A342701.

Extensions

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