A048520 -id:A048520 - cp's OEIS frontend

A320882 Primes p such that repeated application of A062028 (add sum of digits) yields two other primes in a row: p, A062028(p) and A062028(A062028(p)) are all prime.

11, 59, 101, 149, 167, 257, 277, 293, 367, 419, 479, 547, 617, 727, 839, 1409, 1559, 1579, 1847, 2039, 2129, 2617, 2657, 2837, 3449, 3517, 3539, 3607, 3719, 4217, 4637, 4877, 5689, 5779, 5807, 5861, 6037, 6257, 6761, 7027, 7489, 7517, 8039, 8741, 8969, 9371, 9377, 10667, 10847, 10937, 11257, 11279, 11299, 11657

Offset: 1

M. F. Hasler, Nov 06 2018

"Iterates" the idea of A048519 (p and A062028(p) are prime), also considered in A048523, A048524, A048525, A048526, A048527. (This is the union of A048524, A048525, A048526, A048527 etc. A048525(1) = 277 = a(7).)

Robert Israel, Table of n, a(n) for n = 1..10000

Subsequence of A048519: p and A062028(p) are prime.
Cf. A047791, A048520, A006378, A107740, A243441 (p and p + Hammingweight(p) are prime), A243442 (analog for p - Hammingweight(p)).
Cf. A048523, ..., A048527, A320878, A320879, A320880: primes starting a chain of length 2, ..., 9 under iterations of A062028(n) = n + digit sum of n.

f:= n -> n + convert(convert(n,base,10),`+`):
filter:= proc(n) local x;
if not isprime(n) then return false fi;
x:= f(n);
isprime(x) and isprime(f(x))
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Dec 17 2020

is_A320882(n,p=n)=isprime(p=A062028(p))&&isprime(A062028(p))&&isprime(n) \\ Putting isprime(n) to the end is more efficient for the frequent case when the terms are already known to be prime.
forprime(p=1,14999,isprime(q=A062028(p))&&isprime(A062028(q))&&print1(p","))

A214837 Primes not expressible as the sum of a prime and its digit sum.

Original entry on oeis.org

2, 3, 5, 7, 11, 19, 23, 31, 37, 41, 43, 53, 59, 67, 71, 89, 97, 101, 109, 127, 131, 139, 149, 151, 157, 167, 179, 193, 197, 199, 211, 223, 227, 229, 233, 239, 251, 257, 263, 269, 277, 283, 311, 313, 331, 337, 347, 349, 353, 359, 367, 373, 379, 389, 401, 419

Offset: 1

Jayanta Basu, May 03 2013

Primes not in A048520.

			19 is in the list since there exists no prime p such that p+digit sum of p = 19.

Cf. A006378, A048520.

primeList = Prime[Range[81]]; Complement[primeList, Sort[Select[Table[p + Total[IntegerDigits[p]], {p, primeList}], PrimeQ]]]

A225519 Primes of the form p + sum of squares of digits of p, where p is prime.

Original entry on oeis.org

13, 23, 41, 67, 101, 103, 113, 131, 157, 181, 191, 227, 281, 379, 421, 457, 461, 467, 547, 659, 677, 677, 751, 809, 811, 829, 839, 877, 1039, 1039, 1091, 1093, 1109, 1187, 1201, 1223, 1319, 1361, 1439, 1453, 1531, 1567, 1571, 1613, 1663, 1693, 1753, 1789

Offset: 1

Jayanta Basu, May 09 2013

Primes generated by A076162.

			41 is a member since 41=31+(3^2+1^2).

Cf. A048519, A048520, A076162.

Sort[Select[Table[p=Prime[n]; p+Total[IntegerDigits[p]^2],{n,262}],PrimeQ]]

cp's OEIS Frontend

A320882 Primes p such that repeated application of A062028 (add sum of digits) yields two other primes in a row: p, A062028(p) and A062028(A062028(p)) are all prime.

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A214837 Primes not expressible as the sum of a prime and its digit sum.

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A225519 Primes of the form p + sum of squares of digits of p, where p is prime.

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Mathematica