

A032758


Undulating primes (digits alternate).


38



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, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 18181, 32323, 35353, 72727, 74747, 78787, 94949, 95959, 1212121, 1616161, 323232323, 383838383
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OFFSET

1,1


COMMENTS

Sometimes called "smoothly undulating primes", to distinguish them from A059168.


REFERENCES

C. A. Pickover, "Keys to Infinity", Wiley 1995, p. 159,160.
C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123124, 316317.


LINKS

Michael S. Branicky, Table of n, a(n) for n = 1..131 (terms 1..100 from Sean A. Irvine)
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
Charles W. Trigg, Ninedigit patterned palindromic primes, Crux Mathematicorum, Vol. 7, No. 6, June  July 1981, pp. 168170.


MATHEMATICA

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 *)


PROG

(Python)
from itertools import count, islice
from sympy import isprime, primerange
def agen(): # generator of terms
yield from (p for p in primerange(2, 100) if p != 11)
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))
print(list(islice(agen(), 51))) # Michael S. Branicky, Jun 09 2022


CROSSREFS

Cf. A033619, A030291, A059168, A242541, A004022.
Sequence in context: A308078 A050757 A059168 * A106118 A029743 A344620
Adjacent sequences: A032755 A032756 A032757 * A032759 A032760 A032761


KEYWORD

nonn,base,easy


AUTHOR

Patrick De Geest, May 15 1998


EXTENSIONS

Sequence corrected by JuriStepan Gerasimov, Jan 28 2010
Offset corrected by Arkadiusz Wesolowski, Sep 13 2011


STATUS

approved



