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A172508 Prime numbers such that the differences between any pair of digits is prime. 3
2, 3, 5, 7, 13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 163, 257, 461, 479, 503, 613, 631, 641, 683, 853, 863, 947, 2749, 4297, 4729 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
No further term between 4729 and 7368787 = A000040(500000). - R. J. Mathar, Feb 16 2010
As Robert G. Wilson v points out, there are only 4 different single-digit primes, 2, 3, 5 and 7. Therefore the difference between any pair of a term cannot be zero; the terms can only have a maximum of 5 different digits. A full search covering this range shows that the sequence terminates with the 4729. - R. J. Mathar, Feb 25 2010
LINKS
MAPLE
isA172508 := proc(n) local res, dgs, k, l ; dgs := convert(n, base, 10) ; if nops(dgs) < 2 or not isprime(n) then return false; else for k from 1 to nops(dgs)-1 do for l from k+1 to nops(dgs) do if not isprime(abs( op(k, dgs)-op(l, dgs) )) then return false; end if; end do ; end do ; end if; return true; end proc: for i from 1 to 500000 do p := ithprime(i) : if isA172508(p) then printf("%d, \n", p) ; end if; end do: # R. J. Mathar, Feb 16 2010
MATHEMATICA
Select[Prime[Range[638]], And@@PrimeQ[#[[1]]-#[[2]]&/@ Subsets[ IntegerDigits[ #], {2}]]&] (* Harvey P. Dale, Nov 29 2012 *)
CROSSREFS
Sequence in context: A115261 A063792 A270391 * A272107 A227880 A167134
KEYWORD
nonn,base,fini,full
AUTHOR
Claudio Meller, Feb 05 2010
EXTENSIONS
Three more terms from R. J. Mathar and Robert G. Wilson v, Feb 16 2010
Edited by N. J. A. Sloane, Feb 24 2010
Keywords:fini,full added by Ray Chandler and R. J. Mathar, Feb 25 2010
STATUS
approved

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Last modified March 2 07:05 EST 2024. Contains 370460 sequences. (Running on oeis4.)