Discussion
Sun Nov 03
15:57
Jon E. Schoenfield: Ah! Good point. Thanks!
Discussion
Sun Nov 03
11:38
Joerg Arndt: Just this: keyword "base"?
NAME
Numbers k such that (89*10^(k-1) + 1)/9 is both a plateau and depression prime.
EXAMPLE
a(n)k=7 -> (89*10^(7-1) + 1)/9 = 8*(10^7 - 1)/9 + (10^6 + 1) = 8888888 + 1000001 = 9888889.
Discussion
Thu Oct 31
02:24
Jon E. Schoenfield: I've taken the step of removing the "plateau" part from the Name because I think the primes corresponding to the terms in the sequence are all what the author of this sequence referred to as "depression primes".
Source: http://www.worldofnumbers.com/deplat.htm#pdp989
==============================
Plateau and Depression Primes (or PDP's for short) are numbers that are primes, palindromic in base 10, and consisting of a repdigital interior bordered by two identical single digits D different from the repdigit R.
D_RRR...RRR_D or D(R)nD
We have Plateau Primes when D < R
We have Depression Primes when D > R
E.g.
101
3222223
74444444447
79999999999999999999999999997
==============================
So -- if I'm understanding correctly -- the examples above would be categorized as follows:
101: depression prime (1 > 0)
3222223: depression prime (3 > 2)
74444444447: depression prime (7 > 4)
79999999999999999999999999997: plateau prime (7 < 9)
So, if this is correct, then since this sequence (A082719) gives primes of the form
988888...888889 (9 > 8)
... they're all depression primes.
Does this seem correct?
NAME
Union of (numbers k such that 8*(10^k-1)/9 + 10^(k-1) + 1 is both a plateau and depression prime) and (numbers Numbers k such that (89*10^(k-1)+1)/9 is both a plateau and depression prime).
Discussion
Wed Oct 30
02:58
Michel Marcus: euh .... but 8*(10^k-1)/9 + 10^(k-1) + 1 and (89*10^(k-1)+1)/9 are two expressions that give the same numbers ... ??
10:57
Bruno Berselli: Yes... 8*(10^k-1)/9 + 10^(k-1) + 1 = (89*10^(k-1)+1)/9.
13:22
Michel Marcus: I think one could use one (of the 2) expression in the name; and say in comment that this expression can also be written as 2nd expression
13:23
Michel Marcus: or like this ? Numbers k such that 8*(10^k-1)/9 + 10^(k-1) + 1 (or (89*10^(k-1)+1)/9) is a plateau and depression prime.
13:31
N. J. A. Sloane: I wondered about that. Will fix.
Discussion
Wed Oct 30
02:20
Joerg Arndt: While the new name is not great to read, it is clear.
NAME
Numbers Union of (numbers k such that 8*(10^k-1)/9 + 10^(k-1) + 1 or is both a plateau and depression prime) and (numbers k such that (89*10^(k-1)+1)/9 is both a plateau and depression prime).
Discussion
Wed Oct 30
01:08
N. J. A. Sloane: Jon, Is this better? Worse?
