A048177 Primes p = d_1 d_2 ... d_k in base 10 such that for some base b, p = Sum_{i = 1..k} b^d_i.

101, 1033, 101111, 1010203, 11111101, 101001001, 111010111, 1110011101, 1110110011, 10000110011, 10001000011, 10001001011, 10001011001, 10010000111, 10010001011, 10010100101, 10011000011, 10100000011, 10100000111, 10100011001, 10100101001, 10100110001, 10101111011, 10110000101, 10110100001, 10111000001, 10111202111, 11000010011, 11000010101, 11010000101, 11011011001, 11011101011, 11100000101

Offset

1,1

Links

Max Alekseyev, Table of n, a(n) for n = 1..180

Carlos Rivera, Puzzle 32. Find couples of numbers like this (1033, 8) such that 1033 = 8^1+8^0+8^3+8^3, The Prime Puzzles & Problems Connection.

Example

101=50^1+50^0+50^1

Mathematica

isValid[n_]:= Module[{digits, b, totalSum, dcount}, If[ !PrimeQ[n], Return[False]]; digits=IntegerDigits[n]; dcount=DigitCount[n]; If[Total[dcount[[{2, 3, 4, 5, 6, 7, 8, 9}]]]==0, dcount=DigitCount[n]; If[Mod[n-dcount[[10]], dcount[[1]]]==0, Return[True], Return[False]]; ]; b=0; totalSum=0; While[totalSum<n, b++; totalSum=Total[b^digits]; ]; If[totalSum==n, Return[True], Return[False]]; ]; For[i=1, i<1000000, i++, If[isValid[i], Print[i]]; ]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 17 2006 *)

Crossrefs

Cf. A048178.

Sequence in context: A131194 A124015 A099182 * A283504 A267270 A280340

Adjacent sequences: A048174 A048175 A048176 * A048178 A048179 A048180

Keyword

base,nonn

Author

Felice Russo and Patrick De Geest

Extensions

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 17 2006

Terms a(10) onward from Max Alekseyev, Mar 18 2023

Status

approved