A059168 Primes in which digits alternately rise and fall (or vice versa); sometimes called undulating primes.

2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 131, 151, 163, 173, 181, 191, 193, 197, 241, 251, 263, 271, 281, 283, 293, 307, 313, 317, 353, 373, 383, 397, 401, 409, 419, 439, 461, 463, 487, 491

Offset

1,1

References

C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123-124, 316-317.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Maple

extend:= proc(n) local L, j;
  L:= convert(n, base, 10);
  if (L[-1] < L[-2]) xor (nops(L)::odd) then
    seq(10*n+j, j=0..L[1]-1)
  else
    seq(10*n+j, j=L[1]+1..9)
  fi
end proc:
und[2]:= [seq(seq(10*i+j, j=subs(i=NULL, [$0..9])), i=1..9)]:
for i from 3 to 4 do und[i]:= map(extend, und[i-1]) od:
select(isprime, [2, 3, 5, 7, seq(op(und[i], i=2..4)]); # Robert Israel, Nov 15 2018

Mathematica

d[n_]:=Differences[IntegerDigits[n]]; mQ[n_]:=MemberQ[d[n], 0]==False; a[n_]:=DeleteDuplicates[Sign[Take[d[n], {1, -1, 2}]]]; b[n_]:=DeleteDuplicates[Sign[Take[d[n], {2, -1, 2}]]]; t={}; Do[p=Prime[n]; If[mQ[p], If[Length[IntegerDigits[p]]<=2, AppendTo[t, p], If[Length[a[p]]==Length[b[p]]==1 && a[p][[1]]!=b[p][[1]], AppendTo[t, p]]]], {n, 95}]; t (* Jayanta Basu, May 08 2013 *)
Table[Which[p<10, p, p<100&&Differences[IntegerDigits[p]]!={0}, p, p>100&&Union[Total/@ Partition[Sign[Differences[IntegerDigits[p]]], 2, 1]]=={0}, p, True, Nothing], {p, Prime[ Range[ 150]]}] (* Harvey P. Dale, Aug 07 2023 *)

Prog

(Python)
from sympy import isprime
def f(w, dir):
    if dir == 1:
        for s in w:
            for t in range(int(s[-1])+1, 10):
                yield s+str(t)
    else:
        for s in w:
            for t in range(0, int(s[-1])):
                yield s+str(t)
A059168_list = []
for l in range(5):
    for d in '123456789':
        x = d
        for i in range(1, l+1):
            x = f(x, (-1)**i)
        A059168_list.extend([int(p) for p in x if isprime(int(p))])
        if l > 0:
            y = d
            for i in range(1, l+1):
                y = f(y, (-1)**(i+1))
            A059168_list.extend([int(p) for p in y if isprime(int(p))]) # Chai Wah Wu, Apr 25 2021

Crossrefs

Cf. A032758, A059170.

Sequence in context: A243535 A308078 A050757 * A032758 A106118 A029743

Adjacent sequences: A059165 A059166 A059167 * A059169 A059170 A059171

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Feb 14 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Feb 15 2001

Offset changed by Robert Israel, Nov 15 2018

Status

approved