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A032758 Undulating primes (digits alternate).

%I A032758 #35 Jun 10 2022 06:15:15
%S A032758 2,3,5,7,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
%T A032758 101,131,151,181,191,313,353,373,383,727,757,787,797,919,929,18181,
%U A032758 32323,35353,72727,74747,78787,94949,95959,1212121,1616161,323232323,383838383
%N A032758 Undulating primes (digits alternate).
%C A032758 Sometimes called "smoothly undulating primes", to distinguish them from A059168.
%D A032758 C. A. Pickover, "Keys to Infinity", Wiley 1995, p. 159,160.
%D A032758 C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123-124, 316-317.
%H A032758 Michael S. Branicky, <a href="/A032758/b032758.txt">Table of n, a(n) for n = 1..131</a> (terms 1..100 from Sean A. Irvine)
%H A032758 C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&amp;format=complete">Zentralblatt review</a>
%H A032758 Charles W. Trigg, <a href="https://cms.math.ca/wp-content/uploads/crux-pdfs/Crux_v7n06_Jun.pdf">Nine-digit patterned palindromic primes</a>, Crux Mathematicorum, Vol. 7, No. 6, June - July 1981, pp. 168-170.
%t A032758 a[n_] := DeleteDuplicates[Take[IntegerDigits[n],{1,-1,2}]]; b[n_] := DeleteDuplicates[Take[IntegerDigits[n],{2,-1,2}]]; t={}; Do[p=Prime[n]; If[p<10, AppendTo[t,p], If[Length[a[p]] == Length[b[p]] == 1 && a[p][[1]] != b[p][[1]], AppendTo[t,p]]], {n,3*10^7}]; t (* _Jayanta Basu_, May 04 2013 *)
%o A032758 (Python)
%o A032758 from itertools import count, islice
%o A032758 from sympy import isprime, primerange
%o A032758 def agen(): # generator of terms
%o A032758     yield from (p for p in primerange(2, 100) if p != 11)
%o A032758     yield from (t for t in (int((A+B)*d2+A) for d2 in count(1) for A in "1379" for B in "0123456789" if A != B) if isprime(t))
%o A032758 print(list(islice(agen(), 51))) # _Michael S. Branicky_, Jun 09 2022
%Y A032758 Cf. A033619, A030291, A059168, A242541, A004022.
%K A032758 nonn,base,easy
%O A032758 1,1
%A A032758 _Patrick De Geest_, May 15 1998
%E A032758 Sequence corrected by _Juri-Stepan Gerasimov_, Jan 28 2010
%E A032758 Offset corrected by _Arkadiusz Wesolowski_, Sep 13 2011