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A070029
Primes with only prime digits and whose initial, all intermediate and final iterated sums of digits are primes.
1
2, 3, 5, 7, 23, 223, 227, 353, 2333, 2777, 3323, 7727, 27527, 33377, 33773, 35537, 35573, 35753, 37337, 52727, 53777, 55337, 55373, 55733, 57557, 57737, 57773, 73553, 73757, 75227, 75353, 75377, 75533, 75557, 75773, 77573, 222557, 222773
OFFSET
1,1
COMMENTS
This sequence is the intersection of A062088 and A070027.
EXAMPLE
53777 is a term because 53777 is a prime with only prime digits and 5+3+7+7+7=29, 2+9=11 and 1+1=2 are all prime.
MATHEMATICA
iifpQ[n_]:=AllTrue[NestWhileList[Total[IntegerDigits[#]]&, n, #>9&], PrimeQ]; Select[Prime[Range[20000]], AllTrue[IntegerDigits[#], PrimeQ]&&iifpQ[#]&] (* Harvey P. Dale, Jul 18 2021 *)
CROSSREFS
Cf. A070027, A062088 (only first sum of digits is necessarily prime).
Sequence in context: A289754 A062088 A343834 * A360497 A368805 A262339
KEYWORD
base,nonn
AUTHOR
Rick L. Shepherd, Apr 21 2002
STATUS
approved