A032758 Undulating primes (digits alternate).

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

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. 123-124, 316-317.

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, Nine-digit patterned palindromic primes, Crux Mathematicorum, Vol. 7, No. 6, June - July 1981, pp. 168-170.

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 Juri-Stepan Gerasimov, Jan 28 2010

Offset corrected by Arkadiusz Wesolowski, Sep 13 2011

Status

approved