A048528 Primes expressible in two ways as the sum of an integer and its digit sum.

101, 103, 107, 109, 113, 307, 311, 313, 317, 509, 521, 709, 719, 911, 919, 1009, 1013, 1213, 1217, 1409, 1607, 1609, 1613, 1619, 1621, 1811, 1823, 2017, 2027, 2111, 2113, 2309, 2311, 2521, 2711, 2713, 2719, 2917, 2927, 3011, 3209, 3217, 3221, 3407, 3413, 3613, 3617, 3623

Offset: 1

Author

Patrick De Geest, May 15 1999

Keywords

• nonn
• base
• nice

Examples

			313 = 296 + (2+9+6) and 313 = 305 + (3+0+5).
		

Links

• Delbert L. Johnson, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A047791, A048521.

Programs

Mathematica

Transpose[Select[Tally[Select[#+Total[IntegerDigits[#]]&/@ Range[ 5000], PrimeQ]],#[[2]]==2&]][[1]] (* Harvey P. Dale, May 09 2013 *)

Python

from collections import Counter
from sympy import isprime
def a_list(upto):
    return [i for i, j in Counter([i+sum(map(int, str(i))) for i in range(upto)]).items() if j>1 and isprime(i)]
print(a_list(4000)) # Nicholas Stefan Georgescu, Mar 02 2023

Extensions

Corrected and extended by Harvey P. Dale, May 09 2013