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
Examples
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;
...
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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
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.
Extensions
More terms from Robert Israel, Feb 11 2018