A137923 Zerofree numbers k such that A061486(k) is prime.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A052382, A061486.

Sequence in context: A117288 A117283 A198096 * A163753 A131930 A230918

Adjacent sequences: A137920 A137921 A137922 * A137924 A137925 A137926

Keyword

easy,nonn,base

Author

Ctibor O. Zizka, Apr 30 2008

Extensions

More terms from Robert Israel, Feb 11 2018

Status

approved