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A137923
Zerofree numbers k such that A061486(k) is prime.
3
2, 3, 5, 7, 11, 12, 13, 15, 16, 18, 19, 21, 23, 25, 27, 29, 31, 32, 34, 35, 37, 43, 45, 51, 52, 53, 54, 56, 57, 58, 59, 61, 65, 72, 73, 75, 78, 79, 81, 85, 87, 89, 91, 92, 95, 97, 98, 212, 213, 216, 218, 219, 223, 225, 229, 232, 233, 235, 236, 239, 243, 245, 249, 255, 256, 269, 272, 273, 278, 283
OFFSET
1,1
LINKS
FORMULA
Members of the sequence are numbers n = X(1)...X(r) for which digits the following equation holds: (X(1) + ... + X(r)) + (X(1)*X(2) + ... + X(r-1)*X(r)) + ... + (X(1)*...*X(r)) = p, where p is a prime number, X(i) is the i-th digit of n, and every digit is nonzero.
EXAMPLE
2-digit numbers are of the form X(1)X(2).
The equation is then X(1) + X(2) + X(1)*X(2) = p, where p is prime and both digits are nonzero. Power set is {();(1);(2);(1,2)}, so indices of digits in the equation are running through the power set.
Following numbers n are solutions of the equation:
11 because 1 + 1 + 1*1 = 3;
12 (and its reverse, 21) because 1 + 2 + 1*2 = 5;
13 (and its reverse, 31) because 1 + 3 + 1*3 = 7;
15 (and its reverse, 51) because 1 + 5 + 1*5 = 11;
16 (and its reverse, 61) because 1 + 6 + 1*6 = 13;
18 (and its reverse, 81) because 1 + 8 + 1*8 = 17;
19 (and its reverse, 91) because 1 + 9 + 1*9 = 19;
23 (and its reverse, 32) because 2 + 3 + 2*3 = 11;
25 (and its reverse, 52) because 2 + 5 + 2*5 = 17;
...
MAPLE
filter := proc (n) local L; L := convert(n, base, 10); not has(L, 0) and isprime(add(add(convert(L[i .. j], `*`), i = 1 .. j), j = 1 .. nops(L))) end proc:
select(filter, [$1..1000]); # Robert Israel, Feb 11 2018
CROSSREFS
Sequence in context: A117288 A117283 A198096 * A163753 A131930 A230918
KEYWORD
easy,nonn,base
AUTHOR
Ctibor O. Zizka, Apr 30 2008
EXTENSIONS
More terms from Robert Israel, Feb 11 2018
STATUS
approved