A092621 Primes with exactly one prime digit.
2, 3, 5, 7, 13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 103, 107, 113, 131, 139, 151, 163, 167, 179, 193, 197, 211, 241, 269, 281, 311, 349, 389, 421, 431, 439, 443, 463, 467, 479, 487, 509, 541, 569, 599, 607, 613, 617, 631, 643, 647, 659, 683, 701, 709
Offset: 1
Examples
13 is prime and it has one prime digit, 3; 103 is prime and it has one prime digit, 3.
Links
- Zak Seidov, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Maple
stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end: ts_stpf:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='true') then stpf:=stpf+1; # number of prime digits fi od; RETURN(stpf) end: ts_pr_prn:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( isprime(i)='true' and ts_stpf(i) = 1) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_pr_prn(1000);
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Mathematica
podQ[n_]:=(1==Length@Select[IntegerDigits[n],PrimeQ]);Select[Prime[Range[250]],podQ](* Zak Seidov *)
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PARI
isok(n) = isprime(n) && (d = digits(n)) && (sum(i=1, #d, isprime(d[i])) == 1); \\ Michel Marcus, Mar 10 2014
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Sage
A092621 = list(p for p in primes(1000) if len([d for d in p.digits() if is_prime(d)]) == 1)
Formula
a(n) >> n^1.28 because of the digit restriction