A296236 Prime-slideable numbers: such that a prime can be obtained by moving each digit d by d places either to the left or right, without creating a hole or overlap.

2, 3, 5, 7, 11, 13, 20, 31, 35, 79, 97, 112, 113, 300, 311, 1021, 1124, 1201, 1243, 1333, 1465, 1546, 2011, 2114, 2231, 2312, 2536, 3001, 3122, 3337, 6752, 6877, 7423, 7441, 7687, 7742, 7867, 7966, 8956, 8996, 10031, 10114, 10211, 11113, 11144, 11221, 11300, 11311, 11336, 11354, 11413

Offset

1,1

Comments

A 2-digit number 10a + b is in the sequence if |a - b| = 2 (or 0) and 10b + a is prime.

Links

Table of n, a(n) for n=1..51.

Example

The number 35 is in the sequence because if the digit 3 is moved three places to the left and the digit 5 is moved five places to the left, this results in the number 53 (three place to the left from the initial position, which does not matter), and 53 is prime.

Prog

(PARI) is_A296236(n, d=matdiagonal(n=digits(n)), v=[1..#n]+n)={!n||forvec(s=vector(#n, i, [0, 1]), vecmax(p=v-2*s*d)-vecmin(p)==#p-1&&#p==#Set(p)&&isprime(sum(i=1, #p, 10^(vecmax(p)-p[i])*n[i]))&&return(1))}

Crossrefs

Cf. A296242 (slideable numbers), A296010 (slideable numbers).

Sequence in context: A171574 A354800 A280937 * A357659 A334041 A181172

Adjacent sequences: A296233 A296234 A296235 * A296237 A296238 A296239

Keyword

nonn,base

Author

M. F. Hasler, Dec 09 2017

Status

approved