A032437 Substrings from the right are prime numbers (using only odd digits different from 5).

3, 7, 13, 17, 37, 73, 97, 113, 137, 173, 197, 313, 317, 337, 373, 397, 773, 797, 937, 997, 1373, 1997, 3137, 3313, 3373, 3797, 7937, 9137, 9173, 9337, 9397, 13313, 33797, 39397, 79337, 79397, 91373, 91997, 99137, 99173, 99397, 139397, 379397

Offset: 1

Author

Carlos Rivera

Keywords

• nonn
• fini
• full
• base
• nice

Comments

Primes p with decimal expansion d_1 d_2 d_3 ... d_k such that the digits d_i are 1, 3, 7, or 9, and deleting 1, 2, 3, up to k-1 leading digits also produces a prime. For example, 9173 is a term because all of 9173, 173, 73, and 3 are primes. - N. J. A. Sloane, Jun 28 2022

Examples

			173 is a term because 173, 73, and 3 are all primes. 371 is not a term because 371 and 1 are not primes. - _N. J. A. Sloane_, Jun 28 2022
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..58 [The complete list of terms]
• C. Rivera, Prime strings
• Eric Weisstein's World of Mathematics, Truncatable Prime.

Crossrefs

Cf. A033664, A024785, A020994, A024770, A052023, A052024, A052025, A050986, A050987.

Programs

Mathematica

Select[Prime[Range[33000]],SubsetQ[{1,3,7,9},IntegerDigits[#]]&&AllTrue[Mod[#,10^Range[ IntegerLength[ #]-1]],PrimeQ]&] (* Harvey P. Dale, Jun 28 2022 *)

PARI

is(n)=my(d=digits(n)); for(i=1,n, if(!isprime(fromdigits(d[i..n])), return(0))); 1 \\ Charles R Greathouse IV, Jun 25 2017

Extensions

Single-digit terms added by Eric W. Weisstein.