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A059170 Strictly undulating primes (digits alternate and differ by 1). 1
2, 3, 5, 7, 23, 43, 67, 89, 101, 787, 32323, 78787, 1212121, 323232323, 989898989, 12121212121, 32323232323, 787878787878787878787, 787878787878787878787878787, 1212121212121212121212121212121212121212121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The next two terms have 95 and 139 digits respectively.  [Jayanta Basu, May 09 2013]

REFERENCES

Of form ababa... with |a-b| = 1.

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

Table of n, a(n) for n=1..20.

P. De Geest, More undulating primes

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

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 && Abs[a[p][[1]]-b[p][[1]]] == 1, AppendTo[t, p]]], {n, 10^5}]; t (* Jayanta Basu, May 08 2013 *)

t1=Join[{2, 3, 5, 7}, Select[Range[10, 100], PrimeQ[#]&&Abs[Differences[IntegerDigits[#]]]=={1}&]]; Do[a=n*10+(n-1); b=(n-1)*10+n; t1=Join[t1, Select[Table[(a*10^(2*n+1)-b)/99, {n, 25}], PrimeQ]]; If[n<=7, c=n*10+(n+1); d=(n+1)*10+n; t1=Join[t1, Select[Table[(c*10^(2*n+1)-d)/99, {n, 25}], PrimeQ]]], {n, 1, 9, 2}]; Sort[t1] (* Jayanta Basu, May 09 2013 *)

CROSSREFS

Cf. A032758, A059168, A048398, A033619, A046075, A059758.

Sequence in context: A106711 A235110 A048398 * A068710 A120805 A177119

Adjacent sequences:  A059167 A059168 A059169 * A059171 A059172 A059173

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Feb 14 2001

EXTENSIONS

Extended by Patrick De Geest, Feb 25 2001.

Offset corrected by Arkadiusz Wesolowski, Sep 13 2011

STATUS

approved

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Last modified September 23 21:30 EDT 2017. Contains 292392 sequences.