A107740 -id:A107740 - cp's OEIS frontend

A107741 Smallest number m such that prime(n) = m + (digit sum of m), a(n)=0 if no such m exists.

1, 0, 0, 0, 10, 11, 13, 14, 16, 19, 0, 32, 34, 35, 37, 0, 52, 53, 56, 58, 59, 71, 73, 76, 0, 91, 92, 94, 95, 97, 122, 124, 127, 128, 142, 143, 146, 149, 160, 163, 166, 167, 181, 182, 184, 185, 0, 215, 217, 218, 0, 232, 233, 238, 250, 253, 256, 257, 0, 271

Offset: 1

Reinhard Zumkeller, May 23 2005

If a(n)>0 then: A000040(n)=A062028(a(n)) and A107740(n)>0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A047791, A048521.

Cf. A000040, A055642, A062028.

a107741 n = if null ms then 0 else head ms  where
   ms = [m | let p = a000040 n,
             m <- [max 0 (p - 9 * a055642 p) .. p - 1], a062028 m == p]
-- Reinhard Zumkeller, Sep 27 2014

Data error corrected by Reinhard Zumkeller, Sep 27 2014

A320869 Primes such that p + digitsum(p, base 16) is again a prime.

Original entry on oeis.org

17, 19, 23, 29, 31, 53, 59, 89, 127, 149, 151, 157, 179, 181, 211, 223, 241, 251, 263, 269, 331, 359, 367, 397, 419, 431, 449, 457, 461, 463, 487, 541, 563, 571, 593, 599, 601, 631, 659, 661, 701, 733, 761, 769, 809, 811, 839, 907, 911, 941, 971, 997, 1049, 1087, 1109, 1171, 1201, 1237, 1283, 1289, 1291

Offset: 1

M. F. Hasler, Nov 06 2018

Such primes exist only for an even base b. See A048519, A243441, A320866, A320867 and A320868 for the analog in base 10, 2, 4, 6 and 8, respectively. Also, as in base 10, there are no such primes when + is changed to -, see comment in A243442.

			17 = 16 + 1 = 11[16] (in base 16), and 17 + 1 + 1 = 19 is again prime.

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

Cf. A047791, A048519 (base 10 analog), A048520, A006378, A107740, A243441 (base 2 analog: p + Hammingweight(p) is prime), A243442 (analog for p - Hammingweight(p)), A320866 (analog for base 4), A320867 (analog for base 6), A320868 (analog for base 8).

digsum:= (n,b) -> convert(convert(n,base,b),`+`):
select(p -> isprime(p) and isprime(p+digsum(p,16)), [2,seq(i,i=3..1000,2)]); # Robert Israel, Nov 07 2018

forprime(p=1,1999,isprime(p+sumdigits(p,16))&&print1(p","))

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.

Original entry on oeis.org

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","))

cp's OEIS Frontend

A107741 Smallest number m such that prime(n) = m + (digit sum of m), a(n)=0 if no such m exists.

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A320869 Primes such that p + digitsum(p, base 16) is again a prime.

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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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