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

1,1

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

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A113003 A045423 A214782 * A076746 A243706 A214696

Adjacent sequences: A032434 A032435 A032436 * A032438 A032439 A032440

Keyword

nonn,fini,full,base,nice,changed

Author

Carlos Rivera

Extensions

Single-digit terms added by Eric W. Weisstein.

Status

approved