A256186 -id:A256186 - cp's OEIS frontend

A256227 Naught-y numbers (A011540) that after removing all zeros become zeroless primes (A038618).

20, 30, 50, 70, 101, 103, 107, 109, 110, 130, 170, 190, 200, 203, 209, 230, 290, 300, 301, 307, 310, 370, 401, 403, 407, 410, 430, 470, 500, 503, 509, 530, 590, 601, 607, 610, 670, 700, 701, 703, 709, 710, 730, 790, 803, 809, 830, 890, 907, 970, 1001, 1003, 1007, 1009, 1010, 1013, 1027, 1030

Offset: 1

Charles R Greathouse IV and Zak Seidov, Mar 19 2015

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

A256186 is the intersection of this sequence with A000040.

Cf. A011540, A038618, A056709.

N:= 4: # to produce all terms with <= N digits
ZLO:= proc(d) # produce set of d-digit odd zeroless numbers
       option remember;
       if d = 1 then {1,3,5,7,9}
       else
         map(t -> seq(t+x*10^(d-1),x=1..9), ZLO(d-1))
       fi
end proc:
addzeros:= proc(x,d) # d-digit numbers formed by inserting 0's into x
        local L,n,R;
      L:= convert(x,base,10);
      n:= nops(L);
      R:= map(t -> [op(t),d], combinat[choose](d-1,n-1));
      seq(add(L[i]*10^(r[i]-1),i=1..n), r = R);
    end proc:
Z[1]:= {2,3,5,7}:
for i from 2 to N-1 do Z[i]:= select(isprime,ZLO(i)) od:
`union`(seq(seq(map(addzeros,Z[i],d), i=1..d-1),d=2..N));
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%,list)); # Robert Israel, Mar 19 2015

ss={};Do[id=IntegerDigits[p];If[Min[id]<1&&PrimeQ[FromDigits[Delete[id,Position[id,0]]]],ss={ss,p}],{p,20,2000}];Flatten[ss]
Select[Range[1200],DigitCount[#,10,0]>0&&PrimeQ[FromDigits[DeleteCases[ IntegerDigits[ #],0]]]&] (* Harvey P. Dale, Jan 01 2024 *)

is(n)=my(d=digits(n),e=select(x->x,d)); #e<#d && isprime(fromdigits(e)) \\ Charles R Greathouse IV, Mar 19 2015

A329737 Cyclops primes that remain prime after being "blinded".

Original entry on oeis.org

101, 103, 107, 109, 307, 401, 503, 509, 601, 607, 701, 709, 809, 907, 11071, 11087, 11093, 12037, 12049, 12097, 13099, 14029, 14033, 14051, 14071, 14081, 14083, 14087, 15031, 15053, 15083, 16057, 16063, 16067, 16069, 16097, 17021, 17033, 17041, 17047, 17053

Offset: 1

Rodolfo Ruiz-Huidobro, Nov 20 2019

There are 14 of these primes with 3 digits and 302 with 5 digits.

			The first term, a(1), is 101 because if you remove the "cyclops' eye" it remains a prime (11) and because 101 is the 1st cyclops prime.
307 is a term because when you remove the "0" it remains a prime: 37.

Rodolfo Ruiz-Huidobro, Table of n, a(n) for n = 1..3194

Intersection of A256186 and A134809.

a:=[]; f:=func; g:=func; for n in [1..20000] do if f(n) and IsPrime(g(n)) then Append(~a,n); end if; end for; a; // Marius A. Burtea, Nov 20 2019

A321151 Primes that yield squares after deletion of their zero digits.

Original entry on oeis.org

409, 1021, 1069, 1201, 1609, 2089, 3061, 5209, 9601, 10069, 10369, 18049, 20089, 20809, 37021, 37201, 40009, 44089, 44809, 50329, 50929, 52009, 59029, 59209, 60889, 62401, 70921, 79201, 96001, 100069, 100609, 101449, 102001, 102769, 103069, 104161, 106129, 106801, 108769, 109321

Offset: 1

Marius A. Burtea, Nov 23 2018

Subsequence of A056709. The squares divisible by 2, 3 or 5 cannot be obtained. Most of the squares obtained seem to be squares of prime or semiprime numbers. Among the first 399 squares obtained are 289 squares of prime numbers, 104 squares of semiprimes and 6 other squares; these squares were obtained by testing the prime numbers up to 10^7. Deletion of the zero digits from primes up to 10^8 yields 929 squares of prime numbers, 506 squares of semiprimes and 47 other squares. Do similar results occur when larger primes are considered?
From David A. Corneth, Nov 26 2018: (Start)
Terms can be obtained by listing squares coprime to 30, inserting zeros between digits, and testing the primality of the resulting numbers.
Records for omega(s) where s is a square producing a term occur at terms 409, 50929, 10713481, 3601722361, 1531869148081, 807916258118689. (End)

			      409 is prime and   49 =  7^2 is a square.
     9601 is prime and  961 = 31^2 is a square.
    20809 is prime and  289 = 17^2 is a square.
    10069 is prime and  169 = 13^2 is a square.
   103069 is prime and 1369 = 37^2 is a square.
  1030069 is prime and 1369 = 37^2 is a square.

David A. Corneth, Table of n, a(n) for n = 1..17124 (terms < 10^10)
David A. Corneth, PARI program

Cf. A000040, A000290, A052041, A056709, A256186.

aQ[n_] := PrimeQ[n] && IntegerQ[Sqrt[FromDigits[Select[IntegerDigits[n], #!=0  &]]]]; Select[Range[100000], aQ] (* Amiram Eldar, Nov 25 2018 *)

isok(p) = isprime(p) && issquare(fromdigits(select(x->x, digits(p)))); \\ Michel Marcus, Nov 26 2018

\\ See Corneth link \\ David A. Corneth, Nov 26 2018

cp's OEIS Frontend

A256227 Naught-y numbers (A011540) that after removing all zeros become zeroless primes (A038618).

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A329737 Cyclops primes that remain prime after being "blinded".

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A321151 Primes that yield squares after deletion of their zero digits.

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