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A096790
Prime numbers which when written in base 7 have a composite digit-sum.
0
4801, 9547, 9601, 11311, 11317, 11941, 11953, 13033, 13327, 13669, 13711, 13963, 13999, 14011, 14251, 14293, 14341, 14347, 14389, 14401, 15091, 15427, 15679, 15727, 15973, 16057, 16063, 16069, 16111, 16267, 16363, 16411, 16447, 16453
OFFSET
1,1
COMMENTS
The digit-sum for a multidigit prime in base 7 must be relatively prime to 6, so if the digit-sum is composite it must be 25, 35, 49, ...
According to Joe Roberts, his son found the first term using the Reed College computer, after Dean Alvis, when he was a high school student in 1968, found that there is no term of this sequence below 2000. - Amiram Eldar, Mar 02 2019
REFERENCES
Richard Crandall and Carl Pomerance, Prime Numbers: A Computational Perspective, Springer New York, 2001, Chapter 3, Exercise 3.1, p. 150.
Joe Roberts, Lure of the Integers, The Mathematical Association of America, 1992, Integer 25, p. 171.
EXAMPLE
4801 = 16666_7 and 1 + 6 + 6 + 6 + 6 = 25;
13033 = 52666_7 and 5 + 2 + 6 + 6 + 6 = 25.
MATHEMATICA
Select[ Prime[ Range[5, 1920]], !PrimeQ[ Plus @@ IntegerDigits[ #, 7]] &] (* Robert G. Wilson v, Aug 20 2004 *)
CROSSREFS
Sequence in context: A254035 A255412 A254791 * A157516 A157628 A214146
KEYWORD
nonn,base
AUTHOR
John L. Drost, Aug 16 2004
EXTENSIONS
More terms from Robert G. Wilson v, Aug 20 2004
Corrected by T. D. Noe, Nov 15 2006
STATUS
approved