A240624
Prime numbers n such that replacing each digit d in the decimal expansion of n with d^d produces a prime. Zeros are not allowed.
Original entry on oeis.org
11, 13, 17, 31, 53, 61, 71, 79, 151, 167, 229, 233, 251, 263, 311, 313, 331, 337, 349, 367, 389, 419, 443, 673, 751, 947, 971, 991, 1433, 1531, 1699, 1733, 1993, 2111, 2141, 2153, 2221, 2333, 2393, 2521, 2833, 2963, 3137, 3167, 3323, 3343, 3371, 3389, 3391
Offset: 1
263 is in the sequence because 263 becomes 44665627 which is also prime, where 44665627 is the concatenation (2^2, 6^6, 3^3) = (4, 46656, 27).
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lst={};f[n_]:=Block[{a=IntegerDigits[n],b="",k=1,l},l=Length[a];While[kHarvey P. Dale, Dec 16 2014 *)
A236303
Prime numbers n such that replacing each digit d in decimal expansion of n with prime(d) produces a prime. Zeros are not allowed.
Original entry on oeis.org
2, 3, 5, 7, 19, 59, 79, 167, 229, 347, 439, 449, 467, 487, 547, 569, 617, 727, 787, 859, 877, 967, 1289, 1399, 1549, 1619, 1699, 1747, 1777, 1879, 1997, 1999, 2129, 2297, 2417, 2437, 2447, 2647, 2659, 2687, 2699, 2729, 2819, 2857, 3119, 3137, 3167, 3229, 3347
Offset: 1
347 is in the sequence because 347 becomes 5717 which is also prime, where 5717 is the concatenation (prime(3),prime(4),prime(7))= (5,7,17).
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lst={}; f[n_]:=Block[{a=IntegerDigits[n], b="", k=1, l}, l=Length[a]; While[k
A240623
Prime numbers n such that replacing each digit d in the decimal expansion of n with d^d produces a prime. Zeros are allowed with the convention 0^0 = 1.
Original entry on oeis.org
11, 13, 17, 31, 53, 61, 71, 79, 151, 167, 229, 233, 251, 263, 311, 313, 331, 337, 349, 367, 389, 409, 419, 443, 673, 751, 947, 971, 991, 1433, 1531, 1699, 1733, 1993, 2011, 2027, 2053, 2063, 2081, 2111, 2141, 2153, 2221, 2333, 2393, 2503, 2521, 2833, 2963
Offset: 1
263 is in the sequence because 263 becomes 44665627 which is also prime, where 44665627 is the concatenation of the numbers (2^2, 6^6, 3^3) = (4, 46656, 27).
2503 is in the sequence because 2503 becomes 43125127 which is also prime, where 43125127 is the concatenation of the numbers (2^2, 5^5, 0^0, 3^3) = (4, 3125, 1, 27).
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with(numtheory):T:=array(1..10):L:=array(1..10):
for n from 1 to 1000 do:
p:=ithprime(n):k:=0:s:=0:j:=0:
x:=convert(p,base,10):n1:=nops(x):
for m from n1 by -1 to 1 do:
k:=k+1:T[k]:=x[k]^x[k]:L[k]:=length(T[k]):
od:
n2:=sum('L[j]', 'j'=1..n1):s2:=0:
for u from n1 by -1 to 1 do:
s2:=s2+T[u]*10^(n2-L[u]):n2:=n2-L[u]:
od:
if type(s2,prime)=true
then
printf(`%d, `,p):
else
fi:
od:
A254928
Smallest (nontrivial) prime that, for each k from 2 to n, remains prime when each digit is replaced by the digit's k-th power.
Original entry on oeis.org
13, 13, 13, 137, 157163, 153391501, 153391501, 1126903901803
Offset: 2
a(5) = 137; (1^k)&(3^k)&(7^k), where "&" represents concatenation of numbers:
for k=2, 1949 (prime), for k=3, 127343 (prime),
for k=4, 1812401 (prime), for k=5, 124316807 (prime).
Cf.
A020449 (primes that contain digits 0 and 1 only).
Cf.
A068492 (primes that remain prime after each digit is replaced by its square).
Cf.
A048393 (replacing digits d in decimal expansion of n with d^3 yields a prime).
A335363
The smallest prime and start of a run of exactly n primes that remain prime after each digit is replaced by its square.
Original entry on oeis.org
2, 19, 13, 131, 2111, 12815137, 103723971119
Offset: 1
a(3)=13 because 13 -> 19 -> 181 are primes and 1641 is composite.
Showing 1-5 of 5 results.
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