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A217063 Primes that remain prime when a single "3" digit is inserted between any two adjacent decimal digits. 3
11, 17, 19, 23, 29, 31, 37, 41, 43, 61, 73, 79, 89, 97, 101, 103, 127, 167, 173, 181, 211, 233, 239, 251, 271, 283, 307, 331, 359, 373, 439, 491, 509, 523, 547, 599, 673, 709, 733, 769, 877, 887, 937, 941, 991, 1033, 1229, 1381, 1619, 1721, 1759, 1789, 1901 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava and Bruno Berselli, Table of n, a(n) for n = 1..1000 (first 275 terms from Paolo Lava)

EXAMPLE

212881 is prime and also 2128831, 2128381, 2123881, 213288 and 2312881.

MAPLE

with(numtheory);

A217063:=proc(q, x)

local a, b, c, i, n, ok;

for n from 5 to q do

  a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1;

    for i from 1 to b-1 do

      c:=a+9*10^i*trunc(a/10^i)+10^i*x;  if not isprime(c) then ok:=0; break; fi; od;

    if ok=1 then print(ithprime(n)); fi; od; end:

A217063(1000000, 3);

PROG

(MAGMA) [p: p in PrimesInInterval(11, 2000) | forall{m: t in [1..#Intseq(p)-1] | IsPrime(m) where m is (Floor(p/10^t)*10+3)*10^t+p mod 10^t}]; // Bruno Berselli, Sep 26 2012

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=3; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217047, A217062-A217065.

Sequence in context: A063449 A157996 A050713 * A038966 A050778 A316100

Adjacent sequences:  A217060 A217061 A217062 * A217064 A217065 A217066

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Sep 26 2012

STATUS

approved

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Last modified September 20 11:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)