cp's OEIS Frontend

A164329 Numbers which yield a prime whenever a zero is inserted between any two digits.

%I A164329 #12 Jun 01 2018 16:11:59
%S A164329 11,13,17,19,37,41,49,53,59,61,67,71,79,89,97,109,113,119,121,131,133,
%T A164329 149,161,169,191,197,203,227,239,253,269,281,283,299,301,319,323,337,
%U A164329 367,379,383,401,403,407,421,449,457,473,493,499,503,509,511,539,551
%N A164329 Numbers which yield a prime whenever a zero is inserted between any two digits.
%C A164329 Single-digit numbers 0, ..., 9 seem to be excluded but would satisfy the condition voidly. - _M. F. Hasler_, May 10 2018
%H A164329 Giovanni Resta, <a href="/A164329/b164329.txt">Table of n, a(n) for n = 1..10000</a>
%e A164329 998471 is in the sequence because all the five numbers 9098471, 9908471, 9980471, 9984071 and 9984701 are primes.
%t A164329 f[n_]:=(r=IntegerDigits[n];l=Length[r];For[k=2,PrimeQ[FromDigits[Insert
%t A164329 [r,0,k]]],k++ ];If[k==l+1,n,0]);Select[Range[11,560],f[ # ]>0&]
%o A164329 (PARI) is(n, L=logint(n+!n, 10)+1, P)={!for(k=1, L-1, isprime([10*P=10^(L-k),1]*divrem(n, P))||return) && n>9} \\ _M. F. Hasler_, May 10 2018
%Y A164329 Cf. A216169 (subset of composite terms), A215417 (subset of primes), A159236 (0 is inserted between all digits).
%Y A164329 Cf. A068679 (1 is prefixed, appended or inserted anywhere), A069246 (primes among these), A068673 (1 is prefixed, or appended).
%Y A164329 Cf. A158594 (3 is prefixed, appended or inserted anywhere), A215419 (primes among these).
%Y A164329 Cf. A069832 (7 is prefixed, appended or inserted anywhere), A215420 (primes among these), A068677 (7 is prefixed or appended).
%Y A164329 Cf. A069833 (9 is prefixed, appended or inserted anywhere), A215421 (primes among these).
%Y A164329 Cf. A158232 (13 is prefixed or appended).
%K A164329 base,easy,nonn
%O A164329 1,1
%A A164329 _Farideh Firoozbakht_, Sep 22 2009
%E A164329 Erroneous comment and cross-references deleted by _M. F. Hasler_, May 10 2018