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A059168
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Primes in which digits alternately rise and fall (or vice versa); sometimes called undulating primes.
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10
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123-124, 316-317.
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LINKS
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C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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)
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))
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Feb 15 2001
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STATUS
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approved
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