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A230087 Primes such that prime plus its digit sum is a perfect square. 1
2, 17, 179, 347, 467, 521, 1433, 1583, 2111, 3347, 10601, 12527, 25889, 28541, 32027, 33113, 39569, 39971, 41201, 43661, 45767, 55667, 58061, 59513, 61001, 62969, 63977, 67061, 70199, 77261, 92387, 92993, 100469, 109541, 120401, 122477, 130307, 156011, 163193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of primes obtained from the sequence ‘prime plus its digit sum is perfect square’ is 150 for n = 1 to 3*10^5, while the sequence for ‘perfect cube’ yields only 11 primes for the same range of n. Hence, sequence for ‘square’ is framed.

Subsequence of primes of A066564. - Michel Marcus, Jun 02 2015

LINKS

K. D. Bajpai and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (terms 2..150 from Bajpai)

EXAMPLE

a(2) = 17 is prime. Digit sum of 17 = 8, 17 + 8 = 25 = 5^2.

a(5) = 467 is prime. Digit sum of 467 = 17, 467 + 17 = 484 = 22^2.

MAPLE

KD:= proc() local a, b, c, d; a:= ithprime(n); b:=add( i, i = convert((a), base, 10))(a); c:=a+b; d:=evalf(sqrt(c)); if d=floor(d) then return (a) :fi; end:seq(KD(), n=1..50000);

PROG

(PARI) for(n=2, 1e4, forprime(p=n^2-9*#digits(n^2), n^2, if(p+sumdigits(p) == n^2, print1(p", ")))) \\ Charles R Greathouse IV, Oct 08 2013

(MAGMA) [p: p in PrimesUpTo(6*10^5) | IsSquare(p+(&+Intseq(p)))]; // Vincenzo Librandi, Jun 02 2015

CROSSREFS

Cf. A048519.

Cf. A107288 (Primes whose digit sum is square).

Sequence in context: A011550 A102023 A212833 * A058010 A242428 A199751

Adjacent sequences:  A230084 A230085 A230086 * A230088 A230089 A230090

KEYWORD

nonn,base,less

AUTHOR

K. D. Bajpai, Oct 08 2013

EXTENSIONS

a(1) from Charles R Greathouse IV, Oct 08 2013

STATUS

approved

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Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)