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A176196 Primes such that the sum of k-th powers of digits, for each of k = 1, 2, 3, and 4, is also a prime. 1
11, 101, 113, 131, 223, 311, 353, 461, 641, 661, 883, 1013, 1031, 1103, 1301, 1439, 1451, 1471, 1493, 1697, 1741, 2111, 2203, 3011, 3347, 3491, 3659, 4139, 4337, 4373, 4391, 4733, 4931, 5303, 5639, 5693, 6197, 6359, 6719, 6791, 6917, 6971, 7411, 7433 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For k = 1, 2, and 3 see A176179

REFERENCES

Charles W. Trigg, Journal of Recreational Mathematics, Vol. 20(2), 1988. "Hands On Numbers Count", Personal Computer World, 1997, p. 290.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

For the prime number n=14549 we obtain :

1 + 4 + 5 + 4 + 9 = 23 ;

1^2 +4^2 + 5^2 +4^2 + 9^2 = 139 ;

1^3 +4^3 + 5^3 +4^3 + 9^3 = 983 ;

1^4 +4^4 + 5^4 +4^4 + 9^4 = 7699 ;

MAPLE

with(numtheory):for n from 2 to 20000 do:l:=evalf(floor(ilog10(n))+1):n0:=n:s1:=0:s2:=0:s3:=0:s4:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s1:=s1+u:s2:=s2+u^2:s3:=s3+u^3:s4:=s4+u^4:od:if type(n, prime)=true and type(s1, prime)=true and type(s2, prime)=true and type(s3, prime)=true and type(s4, prime)=true then print(n):else fi:od:

MATHEMATICA

Select[Prime[Range[1000]], And@@PrimeQ[Total/@Table[IntegerDigits[#]^n, {n, 4}]]&] (* Harvey P. Dale, Jun 16 2013 *)

CROSSREFS

Cf. A176179, A109181, A046704, A052034, A091366.

Sequence in context: A073064 A155075 A176179 * A303570 A208262 A062696

Adjacent sequences:  A176193 A176194 A176195 * A176197 A176198 A176199

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Apr 11 2010

STATUS

approved

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Last modified July 20 15:59 EDT 2019. Contains 325185 sequences. (Running on oeis4.)