A159236 Primes that remain prime when a 0 is inserted between every pair of adjacent digits.

11, 13, 17, 19, 37, 41, 53, 59, 61, 67, 71, 79, 89, 97, 107, 109, 113, 131, 151, 167, 179, 193, 199, 211, 257, 277, 293, 313, 337, 359, 373, 383, 389, 409, 457, 479, 577, 599, 613, 617, 659, 661, 673, 691, 701, 709, 727, 739, 751, 757, 827, 829, 839, 863, 883

Offset: 1

Author

Lekraj Beedassy, Apr 06 2009

Keywords

• nonn
• base

Comments

Prime terms in A050674.

See A119680 for the primes obtained by inserting a 0 between each pair of adjacent digits. - Rémy Sigrist, Oct 08 2017

Examples

			409 is prime, and so is 40009 ( 4(0)0(0)9 ). Hence 409 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A050674, A119680.

Programs

Maple

Lton := proc(L) add( op(i,L)*10^(i-1),i=1..nops(L)) ; end: pad0 := proc(n) dgs := convert(n,base,10) ; L := [op(1,dgs)] ; for i from 2 to nops(dgs) do L := [op(L),0,op(i,dgs)] ; od: Lton(L) ; end: for i from 5 to 400 do p := ithprime(i) ; if isprime( pad0(p) ) then printf("%d,",p) ; fi; od: # R. J. Mathar, Apr 07 2009

Mathematica

Select[Prime[Range[5,200]],PrimeQ[FromDigits[Riffle[ IntegerDigits[ #],0]]]&] (* Harvey P. Dale, Feb 19 2015 *)

Python

from sympy import isprime
def ok(n):
    return n > 10 and isprime(n) and isprime(int("0".join(list(str(n)))))
print([k for k in range(900) if ok(k)]) # Michael S. Branicky, Jul 11 2022

Extensions

Edited by N. J. A. Sloane, Apr 07 2009

Extended by R. J. Mathar, Apr 07 2009