A050498 Arithmetic progressions of at least 4 terms with common difference 6 having the same value of phi(x) start at these numbers.

72, 216, 76326, 101526, 116646, 146886, 298086, 369366, 624966, 1375926, 1532166, 1558086, 1598406, 1750326, 1789206, 1866246, 1991526, 2516406, 2540886, 2620806, 2681286, 2827446, 3151446, 3196806, 3236406, 3489126

Offset: 1

Author

Jud McCranie, Dec 27 1999

Keywords

• nonn

Comments

From Wolfdieter Lang, Jan 11 2021: (Start)

Conjecture: a(n) == 0 (mod 6) for n >= 1. After division by 6 the sequence becomes [12, 36, 12721, 16921, 19441, 24481, 49681, 61561, 104161, 229321, 255361, 259681, 266401, 291721, 298201, 311041, 331921, ...].

6*A163573 is a subsequence. See A163573 for the proof. Note that not all a(n), for n >= 3, are obtained by 6*A163573. The first such term is a(115) = 31850496, and a(115)/6 = 5308416 which is not a prime number, hence not a term of A163573. (End)

Wells gives a wrong value of a(3): 76236. - Stefano Spezia, Sep 08 2024

Examples

			phi(72) = phi(78) = phi(84) = phi(90) = 24, so 72 is in the sequence.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 129.

Links

• Jud McCranie, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A039670, A163573.

Programs

PARI

isok(k) = #Set(vector(4, i, eulerphi(k+(i-1)*6))) == 1; \\ Michel Marcus, Sep 17 2023