A089704 Primes in which the unit place digit is 1 and the k-th most significant digit is prime (2,3,5,7) if k is prime else is composite (4,6,8,9,0).

31, 71, 251, 271, 331, 521, 571, 751, 4231, 4271, 4721, 4751, 6221, 6271, 6521, 6551, 6571, 8221, 8231, 8521, 8731, 9221, 9371, 9521, 9551, 9721, 20231, 20521, 20551, 20731, 20771, 24251, 24371, 24551, 24571, 26251, 26321, 26371, 26731, 28351

Offset

1,1

Links

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

Example

6271 is a member as unit place digit is 1, second MSD is prime, third MSD is prime and the fourth MSD is composite.

Maple

with(combinat, cartprod): ds:=proc(s) local j, l: l:=nops(s): RETURN(add(s[j]*10^(l-j), j=1..l)):end: p:=[2, 3, 5, 7]:c:=[0, 4, 6, 8, 9]: ctpr:=proc(n, s) local m, T, a: a:=s: m:=1: T:=cartprod([seq(piecewise(isprime(n-i+2), p, c), i=2..n), [1]]): while not T[finished] do m:=ds(T[nextvalue]()): if isprime(m) and not member(m, a) then a:=[op(a), m] fi od: RETURN(a): end: a:=[]: for n from 1 to 5 do a:=ctpr(n, a) od: op(a); # C. Ronaldo

Mathematica

rdQ[n_]:=Module[{ridn=Reverse[IntegerDigits[n]]}, Total[Which[#[[1]]==#[[2]] == 1, 1, AllTrue[#, PrimeQ], 1, AllTrue[#, CompositeQ], 1, CompositeQ[#[[2]]] && #[[1]] == 0, 1, True, 0]&/@Table[{ridn[[k]], k}, {k, Length[ ridn]}]] == Length[ ridn]]; Select[Prime[Range[3100]], rdQ] (* Harvey P. Dale, Jan 17 2021 *)

Crossrefs

Cf. A089705.

Sequence in context: A331260 A127345 A127346 * A287609 A210548 A146353

Adjacent sequences: A089701 A089702 A089703 * A089705 A089706 A089707

Keyword

base,nonn

Author

Amarnath Murthy, Nov 10 2003

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

Offset changed by Andrew Howroyd, Sep 17 2024

Status

approved