A052279 -id:A052279 - cp's OEIS frontend

A052286 Primes p such that f(p) > f(q) for all primes q < p, where f(n) is the sum of factorials of the digits of n if that sum is the square of a prime, otherwise f(n)=0.

17, 5077, 178799, 506977979, 4045586999, 156777789899, 157778789899, 1445779999999, 1555899989999, 1556788999999999, 144559999999999699, 156787999999999999, 1444446778999999999999, 1556688999999998999999, 15556699999799999999999, 144444556769999999999999999, 144557778999999999989999999, 177777889899989999999999999, 177778899989999999999999989

Offset: 1

G. L. Honaker, Jr., Feb 07 2000

			a(2)=5077 because 5! + 0! + 7! + 7! = 101^2 (a squared prime that is larger than any of the previous ones).

Max Alekseyev, Table of n, a(n) for n = 1..100

Cf. A000040, A000142, A000290, A052279.

a(4) found by Jud McCranie
a(5)-a(10) from Donovan Johnson, Dec 04 2009
Terms a(11) onward from Max Alekseyev, Feb 14 2024

A290944 Primes p such that sum of digits of p^3 is a perfect square.

Original entry on oeis.org

3, 1753, 1999, 2389, 2713, 3301, 3361, 3529, 3583, 3607, 3631, 3643, 3697, 3889, 3907, 4093, 4099, 4129, 4153, 4159, 4243, 4423, 4591, 4639, 4813, 5167, 5449, 5503, 5527, 5563, 5683, 5689, 5827, 6199, 6211, 6427, 6529, 6553, 6691, 6709, 6883, 6949, 6961, 6997

Offset: 1

K. D. Bajpai, Aug 14 2017

All the terms in this sequence, except a(1), are congruent to 1 mod 3.

After a(1), all the terms are congruent to {1, 4, 7} mod 9.

			a(1) = 3 is prime: 3^3 = 27; 2 + 7 = 9 = 3^2.
a(2) = 1753 is prime: 1753^3 = 5386984777; 5 + 3 + 8 + 6 + 9 + 8 + 4 + 7 + 7 + 7 = 64 = 8^2.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A007605, A052279, A079130, A086924, A235398, A259418, A290843.

[p: p in PrimesUpTo(1000) | IsSquare(&+Intseq(p^3))];

f:= n->add(d, d=convert(n^3, base, 10)):
select(t -> type(sqrt(f(t)), integer), [seq(ithprime(m), m=1..10^3)]);

Select[Prime[Range[2000]], IntegerQ[Sqrt[Plus @@ IntegerDigits[#^3]]] &]

forprime(p=1, 5000, if(issquare(sumdigits(p^3)), print1(p, ", ")));

is(n) = ispseudoprime(n) && issquare(sumdigits(n^3)) \\ Felix Fröhlich, Aug 14 2017

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A052286 Primes p such that f(p) > f(q) for all primes q < p, where f(n) is the sum of factorials of the digits of n if that sum is the square of a prime, otherwise f(n)=0.

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A290944 Primes p such that sum of digits of p^3 is a perfect square.

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