[seqfan] Primes with digits sum 2^k, A068807 and A178796

[Richard Mathar]

Are these two sequences related to prime chains with digit sums the same:

http://oeis.org/classic/?q=id:A178796|id:A068807
2,11,13,17,31,53,71,79,97,101,103,107,211,233,251,277,349,367,431,439,457,503,521,547,619,673,691,701,709,727,853,907,1021,1061,1069,1087,1151,1201,1223,1249,1429,1447,1483,1511,1601,1609,1627,1663,1753,1861,1933,1951,
2,11,13,17,31,53,71,79,97,101,103,107,211,233,251,277,349,367,431,439,457,503,521,547,619,673,691,701,709,727,853,907,1021,1061,1069,1087,1151,1201,1223,1249,1429,1447,1483,1511,1601,1609,1627,1663,1753,1861,

That is: is there a chance that demanding divisibility of digits sums of
adjacent terms in A178796 ever involves a factor >=3 ?