login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319287 Primes of the form x^2 + y^2 where x contains only the decimal digits 0 through 6 (not 7, 8, or 9). 1
5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Pratt shows that this sequence is infinite, and gives an asymptotic formula for a weighting function of a particular subset (see Theorem 1.2). This holds for any choice of at most 3 digits; Pratt comments that by imposing extra conditions on the digits chosen, a more complicated sieve argument can be used to derive a similar result.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Kyle Pratt, Primes from sums of two squares and missing digits, Proceedings of the London Mathematical Society 3:120 (2020), pp. 770-830. arXiv:1806.02699 [math.NT]

EXAMPLE

113 = 7^2 + 8^2 is prime but not in this sequence because both 7 and 8 contain a digit from {7, 8, 9}.

557 = 14^2 + 19^2 is in this sequence because 557 is prime and 14 contains no digit from {7, 8, 9}.

PROG

(PARI) rd(n)=my(v=digits(n)); for(i=1, #v, if(v[i]>6, for(j=i, #v, v[j]=6); return(fromdigits(v, 7)))); fromdigits(v, 7)

list(lim)=my(v=List(), s=sqrtint(lim\=1), s7=rd(s), x2, p); for(w=1, s7, x2=fromdigits(digits(w, 7))^2; forstep(y=(x2%2)+1, sqrtint(lim-L2), 2, if(isprime(p=x2+y^2), listput(v, p)))); Set(v)

CROSSREFS

Subsequence of A002313 and hence of A002144 and hence of A000040.

Cf. A007093.

Sequence in context: A351535 A002144 A280084 * A192592 A349900 A347163

Adjacent sequences:  A319284 A319285 A319286 * A319288 A319289 A319290

KEYWORD

nonn,base

AUTHOR

Charles R Greathouse IV, Oct 10 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 17 15:14 EDT 2022. Contains 356189 sequences. (Running on oeis4.)