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A107934 Numbers n such that n and n-th prime have only one common digit = 3. 4
23, 30, 32, 33, 34, 38, 63, 83, 103, 130, 131, 132, 143, 153, 235, 238, 311, 314, 330, 333, 338, 341, 343, 344, 345, 346, 349, 353, 354, 355, 356, 357, 360, 361, 366, 368, 370, 371, 378, 396, 399, 432, 433, 434, 435, 438, 439, 443, 453, 463, 473, 513, 523 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Other cases of common digit d: A107931 (d=0), A107932 (d=1), A107933 (d=2), A107935 (d=4), A107936 (d=5), A107937 (d=6), A107938 (d=7), A107939 (d=8), A107940 (d=9). Cf. A107930 - smallest m's for digits 0,...,9.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1)=23 because 23rd prime, 83 and 23 have 3 as their only common digit, and 23 is the smallest such number.

MAPLE

filter:= n -> convert(convert(n, base, 10), set) intersect convert(convert(ithprime(n), base, 10), set) = {3}:

select(filter, [$1..1000]); # Robert Israel, May 10 2021

MATHEMATICA

bb={}; Do[If[IntegerDigits [n]\[Intersection]IntegerDigits [ Prime[n]]\[Equal]{3}, bb=Append[bb, n]], {n, 1800}]; bb

CROSSREFS

Cf. A107930 - A107940.

Sequence in context: A068714 A344127 A036267 * A155107 A126719 A110677

Adjacent sequences:  A107931 A107932 A107933 * A107935 A107936 A107937

KEYWORD

nonn,base

AUTHOR

Zak Seidov, May 28 2005

STATUS

approved

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Last modified July 3 06:54 EDT 2022. Contains 355031 sequences. (Running on oeis4.)