A096790 Prime numbers which when written in base 7 have a composite digit-sum.

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.

Links

Table of n, a(n) for n=1..34.

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

Adjacent sequences: A096787 A096788 A096789 * A096791 A096792 A096793

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