A084435 may not be infinite, if it hits a Sierpinski number. The exponents I have are: 0,1,2,1,5,1,1,29,3,37,31,227,835,115, and then it gets stuck. So the 1290-bit 389 digit prime 19668389864872500557560203790497858277784492418873798407026612403944566893365351322116868514901310836920700982678919663050434757651618869728107413733749722845223292398631963057602012174833030924955644631702803467805757838961272217158156264530315202755743516127681944466901139382567960961717373223867237148005010940960999146246286142747282353242557953406503238201229315676231109030713491457 might be special.
Update: the next term is 7615.
The term after that is greater than 4165 (giving up).
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