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

1,1

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A047791, A048521.

Sequence in context: A131687 A327914 A167844 * A164739 A085821 A183087

Adjacent sequences: A048525 A048526 A048527 * A048529 A048530 A048531

Keyword

nonn,base,nice

Author

Patrick De Geest, May 15 1999

Extensions

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

Status

approved